Question

A shell is fired from a cannon with a speed of $100m/s$ at an angle ${30}^o$ with the horizontal (positive $y-$direction). At the highest point of its trajectory, the shell explodes into two equal fragments of masses in the ratio $1:2$.The lighter fragment moves vertically upwards with an initial speed of $200m/s$ .What is the speed of the other fragment at the time of explosion?

Answer 1

Velocity of the connon at the highest point.

$V=100\cos {60}^0$

$V=50$ m/s

Now,

$\varphi$ from momentum conservation

$\Rightarrow m\left(50\right)=m(-50)+mv$

$\Rightarrow V=100m/s$ in positive $X$ direction.