Question

A 90-kg football player jumps vertically into the air to catch a 0.50-kg football that is thrown essentially horizontally at him at 17 m/s. What is his horizontal speed after catching the ball?

a) 0 m/s
b) 34 m/s
c) 17 m/s
d) 1.7 m/s

Answer 1

The horizontal speed of the football player after catching the ball is -0.9456 m/s. Therefore, the correct answer is (d) 1.7 m/s.

Step-by-step explanation:

To find the horizontal speed of the football player after catching the ball, we can use the principle of conservation of momentum. The initial momentum of the system (football player and football) before the catch is zero, since the football is thrown horizontally.

Therefore, the final momentum of the system after the catch must also be zero. Since momentum is calculated using mass and velocity, we can set up the equation:

0 = (90 kg)(vf) + (0.50 kg)(17 m/s)

Solving for vf, we can find the horizontal speed of the football player after catching the ball.

vf = -(0.50 kg)(17 m/s) / (90 kg) = -0.9456 m/s

The negative sign indicates that the football player will have a horizontal speed in the opposite direction of the thrown football. Therefore, the correct answer is (d) 1.7 m/s.