A car is stationary. It accelerates at 0.8 ms^2 for 10 s and then at 0.4 ms^2 for a further 10 s. Use the equations of motion to deduce the car's final displacement. You will have to split the journey into two parts, since the acceleration changes after 10 s.
Answers
Answer:
The final displacement of the car is 140 meters.
Explanation:
The final displacement of the car (\(s\)), in meters, is the sum of the change in displacement associated with each part of the journey, which is derived from the following kinematic formulas:
\(s = s_{1} + s_{2}\) (1)
\(s_{1} = \frac{1}{2}\cdot a_{1}\cdot t_{1}^{2}\) (2)
\(v_{o,2} = a_{1}\cdot t_{1}\) (3)
\(s_{2} = v_{o,2} + \frac{1}{2}\cdot a_{2}\cdot t_{2}^{2}\) (4)
Where:
\(s_{1}\) - Traveled distance of the first part, in meters.
\(s_{2}\) - Traveled distance of the second part, in meters.
\(a_{1}\) - Acceleration in the first part, in meters per square second.
\(a_{2}\) - Acceleration in the second part, in meters per square second.
\(v_{o,2}\) - Initial speed of the car in the second part, in meters per second.
\(t_{1}\) - Time taken in the first part, in seconds.
\(t_{2}\) - Time taken in the second part, in seconds.
If we know that \(a_{1} = 0.8\,\frac{m}{s^{2}}\), \(t_{1} = 10\,s\), \(a_{2} = 0.4\,\frac{m}{s^{2}}\) and \(t_{2} = 10\,s\), then the distance traveled by the car is:
By (2):
\(s_{1} = \frac{1}{2}\cdot \left(0.8\,\frac{m}{s^{2}} \right)\cdot(10\,s)^{2}\)
\(s_{1} = 40\,m\)
By (3):
\(v_{o,2} = \left(0.8\,\frac{m}{s^{2}} \right)\cdot (10\,s)\)
\(v_{o,2} = 8\,\frac{m}{s}\)
By (4):
\(s_{2} = \left(8\,\frac{m}{s} \right)\cdot (10\,s) + \frac{1}{2}\cdot \left(0.4\,\frac{m}{s^{2}} \right)\cdot (10\,s)^{2}\)
\(s_{2} = 100\,m\)
By (1):
\(s = 140\,m\)
The final displacement of the car is 140 meters.
Related Questions
A 0.150-kg rubber stopper is attached to the end of a 1.00-m string and is swung in a circle. If the rubber stopper is swung 2.3 m above the ground and released, how far will the stopper travel horizontally before hitting the ground?
Answers
The stopper travels approximately 4.5 meters horizontally before hitting the ground.
We can use conservation of energy to solve this problem. At the highest point of the stopper's motion, all of its energy is in the form of potential energy, and at the lowest point (when it hits the ground), all of its energy is in the form of kinetic energy.
The potential energy of the stopper at the highest point is:
Ep = mgh
where m is the mass of the stopper, g is the acceleration due to gravity, and h is the height above the ground. Plugging in the values given in the problem, we get:
Ep = (0.150 kg) * (9.81 m/s²) * (2.3 m) ≈ 3.2 J
At the lowest point, all of the potential energy has been converted to kinetic energy:
Ek = (1/2) * mv²
where v is the speed of the stopper just before it hits the ground. Since the stopper is released from rest, we can use conservation of energy to equate the potential energy at the highest point to the kinetic energy just before hitting the ground:
Ep = Ek
mgh = (1/2) * mv²
Solving for v, we get:
v = √(2gh)
where h is the height from which the stopper was released. Plugging in the values given in the problem, we get:
v = √(2 * 9.81 m/s² * 2.3 m) ≈ 6.6 m/s
Now we can use the time it takes for the stopper to fall to the ground to calculate the horizontal distance it travels. The time is given by:
t = √(2h/g)
Plugging in the values given in the problem, we get:
t = √(2 * 2.3 m / 9.81 m/s²) ≈ 0.68 s
During this time, the stopper travels a horizontal distance given by:
d = vt
Plugging in the values we just calculated, we get:
d = (6.6 m/s) * (0.68 s) ≈ 4.5 m
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A wire of a certain length (α = 0.0065 1/°C) has a resistance of 15 Ω at 20°C.
Calculate the temperature at which the resistance will be 22.8 Ω
Answers
The temperature at which the resistance will be 22.8 Ω is 100 °C
How to determine the temperatureThe following data were obtained from the question:
Coefficient of epansion (α) = 0.0065 °C¯¹ Original resistance (R₁) = 15 Ω Original temperature (T₁) = 20 °C New resistance (R₂) = 22.8 ΩNew temperature (T₂) =?The new temperature can be obtained as illustrated below:
α = R₂ – R₁ / R₁(T₂ – T₁)
0.0065 = 22.8 – 15 / 15(T₂ – 20)
0.0065 = 7.8 / 15(T₂ – 20)
Cross multiply
0.0065 × 15 (T₂ – 20) = 7.8
0.0975 (T₂ – 20) = 7.8
Divide both side by 0.0975
T₂ – 20 = 7.8 / 0.0975
T₂ – 20 = 80
Collect like terms
T₂ = 80 + 20
T₂ = 100 °C
Thus, the temperature is 100 °C
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if the truck has four-wheel drive, and the cabinet is wooden, what is it's maximum acceleration (in m/s2)?
Answers
The maximum acceleration will be 4.9 m/s², if the truck has four wheels and the static friction coefficient is 1.
Let the mass of the truck, M
Let the force require to overcome the static friction is F.
Let the acceleration in the forward direction is a.
Coefficient of static friction, μ = 1
4 wheels(2 rear and 2 front wheels) will share the equal force of friction resistance. Force of friction will be equal to the forward force applied by the truck.
That will be F₁/2 = F₂/2 = F
F₁/2 = F₂/2 = μMg/2 = F
μMg/2 = Ma
a = μg/2
a = (1×9.81)/2
a = 4.9 m/s²
--The give question is incomplete, the complete question is:
"The truck has four-wheel drive, and the cabinet is wooden, what is it's maximum acceleration (in m/s2), if the coefficient of static friction is 1?"
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Calculate the orbital period of a satellite circling the Earth at an altitude of 3500 km. Answer to the nearest minute. Show your work.
Answers
The orbital period of the satellite circling the Earth at an altitude of 3500 km is 163 minutes
How do i determine the orbital period?The orbital period for the satellite circling the Earth at an altitude of 3500 km can be obtained as follow:
Altitude = 3500 kmRadius of earth = 6400 KmSemi-major axis (a) = Radius + Altitude = 6400 + 3500 = 9900 Km = 9900 × 1000 = 9900000 mGravitational constant (G) = 6.67×10¯¹¹ Nm²/Kg²Mass of earth (M) = 5.987×10²⁴ KgOrbital period (T) = ?T² = (4π² / GM) × a³
T² = [(4 × 3.14²) / (6.67×10¯¹¹ × 5.987×10²⁴)] × 9900000³
Take the square root of both sides
T = √[((4 × 3.14²) / (6.67×10¯¹¹ × 5.987×10²⁴)) × 9900000³]
T = 9789.15 s
Divide by 60 to express in minutes
T = 9789.15 / 60
T = 163 minutes
Thus, we can conclude that the orbital period of the satellite is 163 minutes
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One object is thrown vertically upward with an initial velocity of 100 m/s and
another object with an initial velocity of 10 m/s. The maximum height reached
by the first object will be _____
that of the other.
a. 10,000 times
b. none of these
c. 1000 times
O d. 100 times
e. 10 times
Answers
We have that for the Question it can be said that The maximum height reached by the first object will be 100 times that of the other.
\((H_{max})_1=100*(H_{max})_2\)From the question we are told
One object is thrown vertically upward with an initial velocity of 100 m/s and another object with an initial velocity of 10 m/s. The maximum height reached by the first object will be
that of the other.
a. 10,000 times
b. none of these
c. 1000 times
d. 100 times
e. 10 times
Generally the equation for the velocity is mathematically given as
\(v=\frac{d}{t}\\\\Where\\\\\frac{H_{max}_1}{H_{max}_2}=\frac{(V_1)^2}{(v_2)^2}\\\\\frac{H_{max}_1}{H_{max}_2}=\frac{10000}{(10}\\\\\)
\((H_{max})_1=100*(H_{max})_2\)
Therefore
The maximum height reached by the first object will be 100 times that of the other.
\((H_{max})_1=100*(H_{max})_2\)
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The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and t in seconds. 10) s = 2t^2 + 2t + 2, 0 < = t < = 2 Find the body?s speed and acceleration at the end of the time interval. [Bonus] Solve the problem. 11) Suppose that f(t) = at^2 + bt + c and f(1) = 21, f?(1) = 7, and f??(1) = 4. Find a, b, and c.
Answers
The values of a, b, and c are 2, 3, and 16, respectively.The given function s = f(t) describes the position of a body as a function of time. To find the body's speed and acceleration at the end of the time interval, we differentiate the position function with respect to time to obtain the velocity function, and then differentiate the velocity function to obtain the acceleration function.
To find the body's speed and acceleration at the end of the time interval, we differentiate the position function s = 2t^2 + 2t + 2 with respect to time.
Taking the derivative, we get the velocity function v = f'(t) = 4t + 2.
Taking the derivative of the velocity function, we get the acceleration function a = f''(t) = 4.
At the end of the time interval (t = 2), we can evaluate the velocity function to find the speed: v(2) = 4(2) + 2 = 10 m/s.
Similarly, we can evaluate the acceleration function to find the acceleration: a(2) = 4 m/s^2.
Therefore, at t = 2, the body's speed is 10 m/s and its acceleration is 4 m/s^2.
11) Given the conditions f(1) = 21, f'(1) = 7, and f''(1) = 4 for the function f(t) = at^2 + bt + c, we can substitute these values into the function and its derivatives to form a system of equations.
Substituting t = 1 into the function, we get f(1) = a(1)^2 + b(1) + c = a + b + c = 21.
Similarly, we substitute t = 1 into the first derivative, f'(1) = 2a(1) + b = 2a + b = 7.
And substituting t = 1 into the second derivative, f''(1) = 2a = 4.
From the third equation, we find that a = 2.
Substituting this value into the second equation, we can solve for b: 2(2) + b = 7, giving b = 3.
Finally, substituting the values of a and b into the first equation, we can solve for c: 2 + 3 + c = 21, giving c = 16.
Therefore, the values of a, b, and c are 2, 3, and 16, respectively.
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If a 0.3% decrease in the price of a good causes its quantity supplied to decrease by 1%, then the supply is: A. Unit elastic B. Elastic C. Inelastic D. Perfectly inelastic
Answers
If a 0.3% decrease in the price of a good causes its quantity supplied to decrease by 1%, then the supply is C. Inelastic.
In this scenario, the supply of the good is considered inelastic. The elasticity of supply measures the responsiveness of the quantity supplied to changes in price. When the price of a good decreases, and the quantity supplied decreases by a larger percentage, it indicates that the supply is relatively unresponsive to price changes.
To determine the elasticity of supply, we compare the percentage change in quantity supplied to the percentage change in price. In this case, a 0.3% decrease in price results in a 1% decrease in the quantity supplied. Since the percentage change in quantity supplied (1%) is greater than the percentage change in price (0.3%), the supply is considered inelastic.
Inelastic supply means that producers are less responsive to price changes, and a small change in price leads to a proportionally smaller change in quantity supplied. In such cases, producers may find it challenging to adjust their output levels quickly in response to price fluctuations.
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A force of 2000N pulls a load at an angle of 60degrees with the horizontal. if the weight of the object is 3000N, Calculate the coefficient of static friction.
Answers
Answer:
If one assumes that F will just start the object to move:
F = μ Wa cos θ where θ is the angle of the applied force
and Wa is the apparent weight of the object
μ = F / (Wa cos θ)
Note that Wa = W - F sin θ true weight less component of applied force
Wa = 3000 - 2000 sin 60 = 1268 N
μ = 2000 / (1/2 * 1268) = 3.15 (seems to be very large, usually < 1)
Explain the difference between music and noise.
Answers
what are three assumptions of the kinetic molecular theory
Answers
1. Gases are composed of a large number of particles that behave like hard, spherical objects in a state of constant, random motion.
2. These particles move in a straight line until they collide with another particle or the walls of the container.
3. These particles are much smaller than the distance between particles. Most of the volume of a gas is therefore empty space.
The air temperature is 70 degrees, and the relative humidity is 90%. Which conclusion can be made?(1 point)
The air holds little water vapor and is relatively dry.
The amount of water vapor in the air is 90% of what the air can hold.
The dew point temperature is 90% of the air temperature.
The temperature must rise in order for air to become saturated with water vapor.
Answers
Answer:
The amount of water vapor in the air is 90% of what the air can hold.
Explanation:
The answer is A
Answer: The answer is B: The amount of water vapor in the air is 90% of what the air can hold
A bowling ball with 218 J of kinetic energy is moving at 8.0 m/s. What is the mass of the bowling ball?
Answers
218= 0.5(m)(8)^2
218= 32m
M= 6.8125
(ii) Let R be a rotation and S be a reflection of the euclidean plane E. Give a precise deion of RS, relating it to the classification of isometries of E². Be careful of special cases.
Answers
RS is a composition of rotation and reflection in the Euclidean plane E². The precise description of RS depends on the specific properties of the rotation R and reflection S.
In general, if R and S have the same axis or line of symmetry, the composition RS results in a translation. If R and S have intersecting lines of symmetry, RS yields a glide reflection. If R and S have perpendicular lines of symmetry, RS produces a rotation.
It is important to consider special cases, such as parallel lines of symmetry, coinciding axes, or perpendicular lines of reflection, as they may lead to different outcomes. The classification of isometries in E² involves understanding how rotations and reflections combine to create different transformations in the plane.
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 A student says that the rods repel because they have poles like magnets, is she correct?
Answers
The student's statement about the rods having poles is not completely accurate, the general idea that objects with the same type of charge will repel each other is correct.
The student is partially correct, but the analogy with magnets is not completely accurate. Like magnets, charged objects have two types of poles, but they are called positive and negative poles. Two objects with the same type of charge (both positive or both negative) will experience a repulsive force, while objects with opposite charges will attract each other.
In the case of the rods which is given, if they are charged with the same type of charge, they will repel each other due to the electrostatic force between them. This force is similar to the magnetic force between two magnets with the same polarity, but the underlying physical principles are different.
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On the periodic table, the elements in the columns have the same number of —
a)protons in their outer shells.
b)electrons in their outer shells.
c)neutrons.
d)electrons.
Answers
Answer:
· Periodic table, in full periodic table of the elements, in chemistry, the organized array of all the chemical elements in order of increasing atomic number —i.e., the total number of protons in the atomic nucleus. When the chemical elements are thus arranged, there is a recurring pattern called the “periodic law” in their properties, in which elements in the same column (group) have similar properties.
its d btw
Which three statements describe electromagnetic waves?
Answers
Answer:
It is most likely option A B and C
Answer:
I think option A ,B,D are correct
A package of batteries cost $8.00. a store reduced the
price to $5.50. what is the percent of decrease? (do not
round).
Answers
The percent of decrease is calculated as 31.25%. To calculate the percent decrease, we need to find the difference between the original price and the reduced price, divide that difference by the original price, and then multiply by 100.
Given: Original price: $8.00
and reduced price: $5.50
1. Find the difference: $8.00 (original price) - $5.50 (reduced price) = $2.50
2. Divide the difference by the original price: $2.50 ÷ $8.00 = 0.3125
3. Multiply by 100 to get the percentage: 0.3125 × 100 = 31.25%
So, the difference: $8.00 - $5.50 = $2.50
Hence, percent decrease: ($2.50 ÷ $8.00) x 100% = 31.25%
So, the percent of decrease in the price of the batteries is 31.25%.
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Kinematics A jet lands on an aircraft carrier at an inisial touchdown speed of 79 m/s. It must slow to a stop in 77 m along the deck of the camier. INCLUDE CORRECT SI UNITS WITH ANSWER. A. Compute the minimum average acceleration required of the jet to stop in the available distance. amin min
= m/s 2
B. Using the acceleration from part A, how much time does it take to stop after touching down? t= s C. What distance will the jet have moved after touching down when its speed has slowed to 20 m/s ? d= m 8. KINEMATICSD 1-D CALCULATIONS [PHY 221 - SUMMER 2022 - SKIP THIS PROBLEM] Kinematics A certain truck can slow at a maximum rate of 4 m/s 2
in an emergency. When traveling in this truck at a constant speed of 17 mis the dirver spots a large hole in the road 44.1 m in from of his position. The truck continues moving forward at a constant speed until the driver applies the brake following a brief delay due to the driver's reaction time. What is the maximum delay due to reaction time the drive can have to enable the truck to stop before it reaches the hole?
Answers
A) The minimum average acceleration required to stop the jet in the given distance is calculated to be -15.25 m/s².
B) Using the acceleration from part A, the time it takes for the jet to stop after touching down is computed to be 5.18 seconds.
C) The distance the jet will have moved after touching down when its speed has slowed to 20 m/s is determined to be 377.8 meters.
A) To find the minimum average acceleration required to stop the jet, we can use the formula for acceleration: acceleration = (final velocity - initial velocity) / time. Plugging in the given values, the acceleration is calculated as\((-79 m/s - 0 m/s) / 77 m = -15.25 m/s^2\). The negative sign indicates that the acceleration is in the opposite direction to the initial velocity.
B) Using the acceleration calculated in part A, we can determine the time it takes for the jet to stop. The formula for time is given by the equation: \(time = (final velocity - initial velocity) / acceleration\). Substituting the values, we have \((0 m/s - 79 m/s) / -15.25 m/s^2 = 5.18 seconds\).
C) To determine the distance the jet will have moved after touching down when its speed has slowed to 20 m/s, we can use the formula for distance: \(distance = initial velocity * time + (1/2) * acceleration * time^2\). Since the jet starts from rest and decelerates, the initial velocity is 0 m/s. Plugging in the values, we get \(distance = 0 m/s * 5.18 s + (1/2) * (-15.25 m/s^2) * (5.18 s)^2 = 377.8 meters\).
Therefore, the jet will have moved a distance of 377.8 meters when its speed slows down to 20 m/s.
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In a closed system of a cannon and cannonball, which changes would both result in an increase in the kinetic energy of the cannonball when fired from the cannon?
Answers
Answer:
the length of the cannon
the power of the gunpowder
Answer:
i would say B decrease mass of cannon or decrease mass of cannon ball
Explanation:
because when you fire the cannon the cannon ball and powder exit the cannon then that leaves the cannon ball and i would say that the explosion would force it out the cannon but would not increase its mass.
22. In an experiment to determine the density of a soil using a density bottle, the following measuren were recorded. Mass of empty density bottle = 42.9g Mass of density bottle full of water = 66.1g Mass of density bottle with some soil = 67.2g Mass of density bottle with soil filled up with water = 82.0g Use the above data to determine the a) Mass of water that completely filled the bottle (2 b) Volume of water that completely filled the bottle
Answers
Answer:1
Explanation:1
Q7 Describe two types of atomic change that produce electromagnetic
waves.
Answers
When an electron drops from a higher energy level to a lower energy level an electromagnetic wave is give off.
Distance is best described as
Please help!!!!
Answers
Answer:
How much an object has moved
State two units bigger than kilogram and how are they related to kilogram
Answers
Answer:
quintal and metric tone.
Explanation:
1 quintal= 100kg
1 metric =1000kg
quintal measures mass of cars, trucks etc, but metric measures bigger things like cargo ships
hope it helps
Increasing the temperature of object by 20K = C *
A. 20 C
B. 293.15 C
C. -253.15 C
D. None of the above
Answers
Answer:
B
Explanation:
the change in velocity over time is called acceleration
Answers
Answer:What' the question?
Explanation:
Answer:
Explanation:
Your answer is correct
a 1500-kg car moving at 9.6 m/s suddenly collides with a stationary car of mass 1700 kg. if the two vehicles lock together, what is their combined velocity immediately after the collision?
Answers
The combined velocity immediately after the collision is 0 m/s. When two objects collide and lock together, the momentum of the two objects is conserved, meaning the final velocity is equal to 0 m/s.
What is the momentum ?
Momentum is a physics concept that describes the motion of an object in terms of its mass and velocity. It is a measure of an object's inertia, or its resistance to changes in its motion. Momentum is a vector quantity, meaning it has both a magnitude (or size) and a direction. The magnitude of an object's momentum is equal to its mass multiplied by its velocity. Momentum is conserved, meaning it can neither be created nor destroyed, only transferred from one object to another. This property is important in many aspects of physics, including collisions, explosions, and the motion of planets. Momentum is also related to force, as a force applied to an object causes its momentum to change.
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ten 7.0-w christmas tree lights are connected in series to each other and to a 120-v source. what is the resistance of each bulb?
Answers
The resistance of each bulb which are connected in series is 20.571 Ω.
Let's find the resistance of each bulb using the given terms:
1. Voltage of source (V_source) = 120 V
2. Number of bulbs (n) = 10
3. Power of each bulb (P) = 7.0 W
We'll use the formula P = V²/R to find the resistance of each bulb.
1: Find the total power of the series.
Total power (P_total) = n * P = 10 * 7.0 W = 70 W
2: Find the total resistance of the series.
Using the formula P_total = V_source^2 / R_total, we can find R_total:
R_total = V_source² / P_total = (120 V)² / 70 W = 14400 / 70 = 205.71 Ω
3: Find the resistance of each bulb.
Since the bulbs are connected in series, the total resistance is the sum of the individual resistances. Therefore, we can find the resistance of each bulb (R_bulb) as follows:
R_bulb = R_total / n = 205.71 Ω / 10 = 20.571 Ω
So, the resistance of each bulb is approximately 20.571 Ω.
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In this experiment, you need to examine the idea of
thermal energy transfer. Using a controlled experiment,
what might a good question about the variables that
affect thermal energy transfer be? Thermal energy
transfer depends on many properties, but limit your
question to only two.
I
Answers
By examining the influence of surface area and material composition on thermal energy transfer in a controlled experiment, we can gain valuable insights into the fundamental factors that affect heat exchange. This knowledge can have practical applications in fields such as engineering, materials science, and energy efficiency.
A good question about the variables that affect thermal energy transfer in a controlled experiment could be: How does the surface area and material composition of an object influence the rate of thermal energy transfer?
By focusing on the surface area and material composition, we can investigate how these two variables affect the transfer of thermal energy. The surface area of an object determines the amount of area available for heat exchange, potentially affecting the rate of energy transfer. The material composition, on the other hand, can impact factors such as thermal conductivity, specific heat capacity, and emissivity, all of which play a role in how effectively heat is transferred.
To conduct the experiment, you can select objects of different materials and surface areas, such as metal plates or plastic blocks with varying dimensions. By exposing them to a controlled heat source and measuring the temperature change over time, you can analyze how the chosen variables affect thermal energy transfer.
This investigation would provide insights into the fundamental factors that influence heat exchange and can be used to inform practical applications in various fields such as engineering, materials science, and energy efficiency.
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A ball is thrown horizontally from the top of
a building 51 m high. The ball strikes the
ground at a point 120 m from the base of the
building.
The acceleration of gravity is 9.8 m/s
2
.
Find the time the ball is in motion.
Answer in units of s.
If the time the ball is in motion is 3.22617 s
Find the initial velocity of the ball.
Answer in units of m/s.
Answers
Answer:
whattt
Explanation:
sorry dear I did not understandjordan has a mass of 65kg and carlos has a mass of 78.0kg. jordan is running at 5.75m/s when he is tackled by carlos who is running in the opposite direction. after the collision of both players are at rest. calculate their velocity before the collision.
Answers
Given
mj = 65 kg
mc = 78 kg
voj = 5.75 m/s
after collision
vfj = vfc = 0 m/s
Procedure
The law of momentum conservation can be stated as follows. For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.
\(\begin{gathered} p_o=p_f \\ m_jv_{0j}-m_cv_{0c}=0 \\ m_jv_{0j}=m_cv_{0c} \\ v_{0c}=\frac{m_jv_{0j}}{m_c} \\ v_{0c}=\frac{65kg*5.75m/s}{78kg} \\ v_{Oc}=4.8m/s \end{gathered}\)
The velocity before the collision would be 4.8m/s