Momentum:

$\overline{){\mathbf{p}}{\mathbf{=}}{\mathbf{m}}{\mathbf{v}}}$

Impulsive force:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{\u2206}\mathbf{p}}{\mathbf{\u2206}\mathbf{t}}}$

The y-component of the velocity does not change. Hence, no change in momentum occurs in the y-direction.

The x-component of the initial velocity is:

A ball of mass *m* moving with velocity *v*⃗ _{i} strikes a vertical wall as shown in (Figure 1) . The angle between the ball's initial velocity vector and the wall is *θ*_{i} 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 Δ*t*, 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 magnitude *F* of the average force exerted on the ball by the wall?

Express your answer in terms of variables given in the problem.

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