We'll use the law of conservation of momentum, which states that the total momentum of an isolated system remains constant.

p_{i} = p_{f}

Initial momentum:

p_{i} = mv_{i}sinθ_{i} - mv_{i}cosθ_{i}

Final momentum:

p_{f} = - mv_{f}sinθ_{f} - mv_{f}cosθ_{f}

Since the Collison is perfectly elastic, the initial velocity is equal to the final velocity.

A ball of mass m moving with velocity v, strikes a vertical wall as shown in (Figure 1). The angle between the ball's initial velocity vector and the wall is θ_{1} as shown on the diagram, which depicts the situation as seen from above. The duration of the collision between the ball and the wall is Δt, and this collision is completely elastic. Friction is negligible, so the ball does not start spinning. In this idealized collision, the force exerted on the ball by the wall is parallel to the x axis.

What is the final angle (θ_{f}) that the ball's velocity vector makes with the negative y axis?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Elastic Collisions concept. You can view video lessons to learn Elastic Collisions. Or if you need more Elastic Collisions practice, you can also practice Elastic Collisions practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Wang's class at New Jersey Institute of Technology.