Question

A 1500 kg weather rocket accelerates upward at 10m/s2. It explodes 2.0 s after liftoff and breaks into two fragments, one twice as massive as the other. Photos reveal that the lighter fragment traveled straight up and reached a maximum height of 530 m. Part A What was the speed of the heavier fragment just after the explosion? Express your answer with the appropriate units.

Answer 1

`V_H=-20.45m/s`

Step-by-step explanation:

By kinematics:

`V_R=V_o+a*t=0+(10m/s^2)*(2s)=20m/s`

The rocket's height at this point is:

`V_R^2=V_o^2+2*a*H_R`

`H_R=20m`

On the lighter fragment:

`V_f^2=V_L^2-2*g*H_L` where Vf=0. Solving for VL:

`V_L=√(2*g*H_L)=100.99m/s`

By conservation of the momentum:

`3*m*V_R=2*m*V_H+m*V_L`

Solving for
`V_H`:

`V_H=(3*V_R-V_L)/(2)=-20.45m/s`