Question

Professional Application. A 96 kg football player catches a 0.900 kg ball with his feet off the ground with both of them moving horizontally. The player's speed is 6.30 m/s, and the ball's speed is 27.4 m/s. First, consider the situation where the player and the ball are going in the same direction, and take this direction as positive. Calculate their final velocity (in m/s). m/s

Answer 1

To solve this problem it is necessary to apply the equations related to the conservation of momentum.

This definition can be expressed as

$m_1u_1+m_2u_2 = (m_1+m_2)V_f$

Where

$m_{1,2}$ = Mass of each object

$u_{1,2}$ = Initial Velocity of each object

$V_f$= Final velocity

Rearranging the equation to find the final velocity we have,

$V_f = \frac{m_1u_1+m_2u_2}{(m_1+m_2)}$

Our values are given as

$m_1 = 96Kg\\m_2 = 0.9Kg\\u_1 = 6.3m/s\\u_2 = 27.4m/s$

Replacing we have,

$V_f = \frac{(96)(6.3)+(0.9)(27.4)}{(96+0.9)}$

$V_f = 6.4959m/s$

Therefore the final velocity is 6.5m/s