Playing in the street, a child accidentally tosses a ball (mass m) with a speed
ID: 1600253 • Letter: P
Question
Playing in the street, a child accidentally tosses a ball (mass m) with a speed of v=19 m/s toward the front of a car (mass M) that is moving directly toward him with a speed of V=19 m/s . Treat this collision as a 1-dimensional elastic collision. After the collision, the ball is moving with speed v back toward the child and the car is moving with speed V in its original direction.
When we combine the equation from Part A with the conservation of momentum equation, we can solve for both final speeds. This relationship will involve the masses of the ball and the car, but we can apply a simplifying assumption: the car is so massive compared with the ball that its speed will not change at all as a result of this collision. Translate this sentence into an equation, what is V equal to? Now, having made this assumption, it becomes possible to solve the equation from Part A for the final speed of the ball, what is it?
Explanation / Answer
part 1:
as speed of the car does not change, V'=V=19 m/s
part 2:
we will consider the direction of car's initial velocity to be positive.
conserving kinetic energy:
0.5*m*v^2+0.5*M*V^2=0.5*m*v'^2+0.5*M*V'^2
==>0.5*m*(v^2-v'^2)=0.5*M*(V'^2-V^2)
as V'=V, v^2-v'^2=0
==> either v=v' or v=-v'
as v=v' is not a valid solution, the correct solution is v=-v'
hence the ball will rebound with the same speed as before the collision i.e. 19 m/s.