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

Answer:

20.015497598 m/s

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

h = 530 m (assumed)

$v=u+at\\\Rightarrow v=0+10\times 2\\\Rightarrow v=20\ m/s$

$s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0\times t+\dfrac{1}{2}\times 10\times 2^2\\\Rightarrow s=20\ m$

$v^2-u^2=2as\\\Rightarrow -u^2=2as-v^2\\\Rightarrow u=\sqrt{v^2-2as}\\\Rightarrow u=\sqrt{0^2-2\times -9.81\times (530-20)}\\\Rightarrow u=100.030995196\ m/s$

As the momentum of the system is conserved

$m_tv_t=m_1v_1+m_2v_2\\\Rightarrow v_2=\dfrac{m_tv_t-m_1v_1}{m_2}\\\Rightarrow v_2=\dfrac{1500\times 20-\dfrac{1}{3}\times 1500\times 100.030995196}{1500\times \dfrac{2}{3}}\\\Rightarrow v_2=-20.015497598\ m/s$

Speed of the heavier fragment is 20.015497598 m/s