First slide

Vertical projection from top of a tower

Question

A ball is projected upwards from the top of a tower with velocity 25 $m s^{- 1}$ . If the height of the tower is 70 m, after what time from the instant of throwing, will the ball reach the ground? (Take, g = 10 $m s^{- 2}$ )

Moderate

A

2 s
B

5 s
C

7 s
D

9 s

Solution

$s_{y} = u_{y} t + \frac{1}{2} a_{y} t^{2} or - 70 = 25 t - 5 t^{2}$
$\Rightarrow 5 t^{2} - 25 t - 70 = 0$
$\Rightarrow t^{2} - 5 t - 14 = 0$
$\Rightarrow t = 7, t = - 2$
$∴ t = 7 s$

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