Question

A ball is projected upwards from the top of tower with a velocity $50m{s}^{-1}$ making an angle ${30}^{\circ }$ with the horizontal. The height of tower is 70 m. After how many seconds from the instant of throwing will the ball reach the ground

• A. 2 s
• B. 5 s
• C. 7 s
• D. 9 s

Answer 1

The correct option is C

7 s

The vertical component of velocity of projection
$=-50sin{30}^{\circ }=-25m/s$
If t be the time taken to reach the ground,
$h=ut+\frac{1}{2}g{t}^2\Rightarrow 70=-25t+\frac{1}{2}\times 10t^2$
$\Rightarrow 70=-25t+5t^2\Rightarrow t^2-5t-14=0\Rightarrow t=-2sand7s$
Since. t=-2 s is not valid $\therefore t=7s$