Question
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.
Answers
Damon
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
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
jeff
teh cop car will destroy the other car because the other car is 300 pounds lighter
Damon
The problem statement says the collision is elastic Jeff. No energy was expended in demolition. The bumpers have magic springs.
ricky
Thanks guys!