Question

Two stones A and B are projected simultaneously from the top of a $100-m$ high tower. Stone B is projected horizontally with speed $10m{s}^{-1}$. and stone A is dropped from the tower. Find out the following:
(a) Time of flight of the two stone
(b) Distance between two stones after 3 s
(c) Angle of strike with ground

Answer 1

a.) To calculate the time of flight (for both stone).apply equation of motion in y-direction.

$100=1/2g{t}^2$

$t=2\sqrt{5}s$

b.)$x_B=10\times 3=30mt$

$y_B=1/2\times g\times t^2$

$=1/2\times 10\times 3\times 3$

$=45m$

Distance between two stones

after $3s$.$x_B=30m,y_B=45m$

c.) Angle of stricking with ground.

$v_y^2=u_y^2+2gh$

$=0+2\times 10\times 100$

$v_y=20\sqrt{5}m{s}^{-1};v_x=10m{s}^{-1}$

$\therefore \overline{v}=v_x\hat{i}+v_y\hat{j}$

$\tan \theta =\frac{v_y}{v_x}$

$\Rightarrow \theta ={\tan }^{-1}\left(\frac{20\sqrt{5}}{10}\right)={\tan }^{-1}\left(2\sqrt{5}\right)$