First slide

Rectilinear Motion

Question

A stone is projected vertically upwards with a speed of $29.4 m / s$ from the top of a tower of height $78.4 m$ . Then the time taken by it to reach the ground is……… $(g = 9.8 m / s^{2})$

Moderate

A

2s
B

8s
C

4s
D

1s

Solution

Given that $h = 78.4 m u = 29.4 m / s$
$∴$ The height of the tower is $h = \frac{1}{2} g t^{2} - u t$
$\begin{array}{l} \Rightarrow 78.4 = \frac{1}{2} \times 9.8 \times t^{2} - 29.4 t \\ \Rightarrow 8 = \frac{t^{2}}{2} - 3 t \\ \Rightarrow t^{2} - 6 t - 16 = 0 \\ ∴ on solving t = 8 s \end{array}$

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