# Why can't a faster object increase its velocity during collision with a slower object?

For an example, a car and a truck are linearly colliding against each other,from opposite directions, and the car is faster than the truck.The collision is perfectly elastic. I do not understand why the car, after colliding and rebounding from the truck, is unable to increase its velocity from its original. Isn't momentum absorbed from the truck? Unless there is a law that i do not understand which states the effect of speed in a collision.

According to AS 9702/12/O/N/17 question 9, and its mark scheme, as reference. (GCE A Levels)

9 A slow vehicle and a fast vehicle travel towards each other in a straight line and then collide. Which outcome is never possible, regardless of the masses of the vehicles?

A. Both vehicles stop
B. Only one vehicle stops
C. The fast vehicle's speed increases
D. The slow vehicle's speed increases

Search for keyword 9702/12/O/N/17 qp for question paper 9702/12/O/N/17 ms for mark scheme

• Two laws must be obeyed at the same time (at all times): momentum conservation and energy conservation. – Steeven Aug 28 '18 at 12:49
• But during collision with a larger object with larger momentum, doesn't it mean that it also holds a lot of kinetic energy which can be transferred into the car, and why wouldn't it abide the law of conservation of energy when kinetic energy from the truck is able to transfer to the car? The total amount of energy in the system may still be the same, but why doesn't the car rebound faster? – user539294 Aug 28 '18 at 12:54
• Please give us a reference to the exact question in the exam. You are right to question this, but it may be because you didn't fully understand what the question says. – alephzero Aug 28 '18 at 13:58
• This sort of question has been asked very many times. You do it in the center of momentum frame. Did you do any searching for how to do collisions? – user93146 Aug 28 '18 at 14:11
• Please send me a link of a question of such, I do not know any questions with similar key words – user539294 Aug 28 '18 at 14:13

The wording of the question is poor, because it doesn't specify what frame is used to measure the velocities.

Taking the "common sense" view that you measure the speed of vehicles relative to the road, the question is simply wrong, since all four options are possible.

If a very light fast moving vehicle collides head on, and elastically, with a heavy slower moving vehicle, the heavy vehicle will continue at (almost) the same speed after the impact, and the light vehicle will rebound at its collision speed relative to the heavy vehicle. So if both vehicles were initially travelling at 10m/s (relative to the road), after the collision the heavy vehicle would still be moving at almost 10m/s, but the light vehicle would rebound at almost 30m/s, again relative to the road. The relative approach speed of the vehicles is 20m/s, and their relative separation speed after the collision is almost the same.

Since the question was set by a British examination board, consider a common demonstration of this in the game of cricket: if a batsman hits a slow bowler back over the bowler's head for six, the speed of the ball (relative to the ground) after the collision with the bat is much faster than its speed before the collision.

In a perfectly elastic collision between a small object and a very large object, the small object will rebound from the large object with the same speed as it had while approaching the large object (but its direction is reversed). To an observer for whom the large object appears stationary, the magnitude of the small object's momentum will not have changed.

However, as you have surmised, for an observer for whom the large object is moving, the velocity of the small object (relative to the observer) will be changed by 2x the velocity of the large object.

• Can you please illustrate it in a diagram? I have a hard time trying to visualize it – user539294 Aug 28 '18 at 13:29
• You have the right idea, but the details of the answer are wrong. If the large object appears stationary before the collision, it will be moving (even if it's only moving slowly) after the collision. The two objects rebound with the same speed and reversed directions, when viewed by an observer for whom the center of mass of both objects is stationary (and by conservation of momentum for the whole system, the CM remains stationary after the collision.) – alephzero Aug 28 '18 at 13:54
• Of course, if the large object is very large and the small object is very small, the center of mass of the system is essentially the center of mass of the large object. – S. McGrew Aug 28 '18 at 14:25
• And then there is the gravitational slingshot used for spacecraft. Those are fully elastic interactions, yet the lighter body ends up going faster. – Jon Custer Aug 28 '18 at 15:02