In a high speed chase, a policeman's car bumps a criminal's car directly from behind to get his attention. The policeman's car is moving at 40 m/s to the right and has a total mass of 1800 kg. The criminal's car is initially moving in the same direction at 38 m/s. His car has a total mass of 1500 kg. Assuming an elastic collision, determine their two velocities immediately after the bump.
u = cop car speed
v = perp car speed
Ui = 40
Vi = 38
initial momentum
= 1800 Ui + 1500 Vi
= 1800(40) + 1500 (38) = 129,000
(same after)
so
129,000 = 1800 u + 1500 v
now Ke
(1/2) 1800 (40)^2+ (1/2)(1500)(38)^2
= (1/2)(1800)(u^2) + (1/2)(1500)(v)^2
or
6(40)^2 + 5(38)^2 = 6 u^2 + 5 v^2
That is two equations with two unknowns. You can solve for u and v
teh cop car will destroy the other car because the other car is 300 pounds lighter
The problem statement says the collision is elastic Jeff. No energy was expended in demolition. The bumpers have magic springs.
Thanks guys!
To determine the velocities of the two cars after the bump, we can use the principles of conservation of momentum and kinetic energy.
1. Start by calculating the initial momentum of each car before the collision. Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). The momentum of an object is a vector quantity, which means it has both magnitude and direction.
For the policeman's car:
Initial momentum of policeman's car = mass of policeman's car * velocity of policeman's car
p1 = (1800 kg) * (40 m/s) = 72,000 kg·m/s (to the right)
For the criminal's car:
Initial momentum of criminal's car = mass of criminal's car * velocity of criminal's car
p2 = (1500 kg) * (38 m/s) = 57,000 kg·m/s (to the right)
2. Since the collision is assumed to be elastic, the total momentum before the collision should be equal to the total momentum after the collision. Therefore, the sum of the initial momenta of both cars should be equal to the sum of their final momenta.
p1 + p2 = p1' + p2'
(72,000 kg·m/s) + (57,000 kg·m/s) = p1' + p2' (where p1' and p2' are the final momenta of the cars)
3. Next, we need to determine the final momentum of each car. To do this, we need to consider the direction of the velocities.
Let's assume that both cars move to the right after the collision. The final momentum of each car can be calculated similarly:
For the policeman's car:
Final momentum of policeman's car = mass of policeman's car * final velocity of policeman's car
p1' = (1800 kg) * v1' (where v1' is the final velocity of the policeman's car)
For the criminal's car:
Final momentum of criminal's car = mass of criminal's car * final velocity of criminal's car
p2' = (1500 kg) * v2' (where v2' is the final velocity of the criminal's car)
4. Now we substitute the expressions for the final momenta into the equation from step 2 and solve the equation for the final velocities.
(72,000 kg·m/s) + (57,000 kg·m/s) = (1800 kg) * v1' + (1500 kg) * v2'
5. Plug in the given values and solve for the final velocities.
(72,000 kg·m/s) + (57,000 kg·m/s) = (1800 kg) * v1' + (1500 kg) * v2'
129,000 kg·m/s = (1800 kg) * v1' + (1500 kg) * v2'
As you can see, without any further information, we cannot solve for the final velocities as there are two unknowns (v1' and v2'). If we had more details about the collision or any other information, we would be able to solve for the final velocities.