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

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the initial horizontal and vertical components of the shell's velocity.
The shell is fired at a speed of \(100 \, \text{m/s}\) at an angle of \(30^\circ\) with the vertical. Therefore, we can find the components of the initial velocity:

- The vertical component \(u_y\):
\[
u_y = 100 \cos(30^\circ) = 100 \times \frac{\sqrt{3}}{2} = 100 \times 0.866 = 86.6 \, \text{m/s}
...