Question

A ball is thrown horizontally from a point $100m$ above the ground with a speed of $200m/s$. Find (a) the time it takes to reach the ground, (b) the horizontal distance it travels before reaching the ground, (c) the velocity (direction and magnitude) with which it strikes the ground.

Answer 1

It is the case of projectile thrown horizontally from a height, in this case

1. Time of flight $T=\sqrt{\left(\frac{2h}{g}\right)}=\sqrt{\frac{2\times 100}{10}}=\sqrt{20}s=2\sqrt{5}=4.47s$
2. Horizontal range,$R=uT=200\times 2\sqrt{5}=400\sqrt{5}m$
3. for velocity we have to calculate both components of velocity along x-axis and y-axis
   

$v_x=u_x=200m/s$ and $v_y=u_y-gT=-10\times 2\sqrt{5}$

so, $v=200m/s\overrightarrow{i}-20\sqrt{5}\overrightarrow{j}$

so angle from horizontal will be , $\theta ={\tan }^{-1}\frac{20\sqrt{5}}{200}={\tan }^{-1}\frac{1}{\sqrt{5}}$