Question

An 80-kg quarterback jumps straight up in the air right before throwing a 0.43-kg football horizontally at 15 m/s . Suppose that the quarterback takes 0.30 s to return to the ground after throwing the ball. How far d will he move horizontally, assuming his speed is constant?

Answer 1

Answer:

0.0241875 m

Explanation:

$m_1$ = Mass of quarterback = 80 kg

$m_2$ = Mass of football = 0.43 kg

$v_1$ = Velocity of quarterback

$v_2$ = Velocity of football = 15 m/s

Time taken = 0.3 seconds

In this system as the linear momentum is conserved

$m_1v_1+m_2v_2=0\\\Rightarrow v_1=-\frac{m_2v_2}{m_1}\\\Rightarrow v_1=-\frac{0.43\times 15}{80}\\\Rightarrow v_1=0.080625\ m/s$

Assuming this velocity is constant

$Distance=Velocity\times Time\\\Rightarrow Distance=0.080625\times 0.3\\\Rightarrow Distance=0.0241875\ m$

The distance the quarterback will move in the horizontal direction is 0.0241875 m