Question

A 1500 kg weather rocket accelerates upward at 10\;{\rm m}/{\rm s}^{2} . It explodes 2.0 s after liftoff and breaks intotwo fragments, one twice as massive as the other. Photos revealthat the lighter fragment traveled straight up and reached amaximum

What was the speed of the heavier fragmentjust after the explosion?

Answer 1

20.015497598 m/s

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

h = 530 m (assumed)

`v=u+at\\\Rightarrow v=0+10* 2\\\Rightarrow v=20\ m/s`

`s=ut+(1)/(2)at^2\\\Rightarrow s=0* t+(1)/(2)* 10* 2^2\\\Rightarrow s=20\ m`

`v^2-u^2=2as\\\Rightarrow -u^2=2as-v^2\\\Rightarrow u=√(v^2-2as)\\\Rightarrow u=√(0^2-2* -9.81* (530-20))\\\Rightarrow u=100.030995196\ m/s`

As the momentum of the system is conserved

`m_tv_t=m_1v_1+m_2v_2\\\Rightarrow v_2=(m_tv_t-m_1v_1)/(m_2)\\\Rightarrow v_2=(1500* 20-(1)/(3)* 1500* 100.030995196)/(1500* (2)/(3))\\\Rightarrow v_2=-20.015497598\ m/s`

Speed of the heavier fragment is 20.015497598 m/s