Two stones are thrown vertically upwards simultaneously from the same point on the ground

Q: Two stones A and B are thrown simultaneously from a point on horizontal ground. The stone A is thrown vertically up with velocity uA and the stone B is thrown with speed uB at angle 37° with horizontal . After 0.9 sec stones are moving perpendicular to each other. Then,

(a) uA > 9ms-1 

(b) uB > 9ms-1 

(c) uB= 15ms-1

(d) uB= 9ms-1 

Sol: Time of Ascent for ball A $\displaystyle t_A = \frac{u_A}{g} $

$\displaystyle \frac{u_A}{g} > 0.9 $

$\displaystyle \frac{u_A}{10} > 0.9 $

$\displaystyle u_A > 9 m/s $

For ball B time of Ascent $\displaystyle t_B = \frac{u_B sin\theta}{g} $

$\displaystyle \frac{u_B sin\theta}{g} = 0.9 $

$\displaystyle \frac{u_B sin37^o}{10} = 0.9 $

$\displaystyle u_B sin37^o = 9 $

$\displaystyle u_B \times \frac{3}{5} = 9 $

$\displaystyle u_B = 15 m/s $