Q. An airplane, diving at an angle of $53.0{^\circ}$ with the vertical releases a projectile at an altitude of 730 m. The projectile hits the ground 5.00 s after being released. What is the speed of the aircraft?

A) $282\ ms^{- 1}$
B) $202\ ms^{- 1}$
C) $182\ ms^{- 1}$
D) $102\ ms^{- 1}$
Explanation

(b) Since the projectile is released its initial velocity is the same as the velocity of the plane at the time of release
Take the origin at the point of release
Let $x$ and $y( = - 730m)$ be the coordinates of the point on the ground where the projectile hits and let $t$ be the time when it hits. Then
$y = - v_{0}t\cos\theta - \frac{1}{2}gt^{2}\ $
where $\theta = 53.0{^\circ}$
This equation gives
$v_{0} = - \frac{y + \frac{1}{2}gt^{2}}{t\cos\theta}$
$= - \frac{- 730 + \frac{1}{2}(9.8)(5)^{2}}{5\cos{53{^\circ}}} = 202\ ms^{- 1}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.