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

0.0241875 m

Step-by-step 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=-(m_2v_2)/(m_1)\\\Rightarrow v_1=-(0.43* 15)/(80)\\\Rightarrow v_1=0.080625\ m/s`

Assuming this velocity is constant

`Distance=Velocity* Time\\\Rightarrow Distance=0.080625* 0.3\\\Rightarrow Distance=0.0241875\ m`

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