Problem 8-82 Impulse-momentum - B

A football of mass $0.41\; kg$ is kicked from rest and given a velocity of $24 \;m/s$ at $29^\circ$ above the horizontal. The ball is in contact with the kicker's foot for $8.2\; m/s.$ Determine:

(a) the horizontal and vertical components of the ball's momentum
(b) the horizontal and vertical components of the average force exerted by the foot on the ball (using momentum methods)
(c) the magnitude and direction of the force in (b).

[Ans. (a) $8.6 \;kg \;m/s; \;4.8 \;kg \;m/s$   (b) $1.0\times 10^3 \;N; 5.8\times 10^2 \;N$   (c) $1.2\times 10^3\; N\; \text{at} \; 29^\circ \; \text{above horizontal}$ ]

Accumulated Solution

Correct!

Any of the four coordinate systems could be used but this is the best.

The initial (i) and final (f) components of momentum are:

Solution $p_{x,i}$ $p_{x,f}$ $p_{y,i}$ $p_{y,f}$
(A) $0$ $mv \sin 29$ $0$ $mv \cos 29$
(B) $mv \cos 29$ $0$ $mv \sin 29$ $0$
(C) $0$ $mv \cos 29$ $0$ $mv \sin 29$
(D) $mv \sin 29$ $0$ $mv \cos 29$ $0$