Question

A ball is projected upwards from the top of tower with a velocity 50 m/s 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

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