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Question
A ball is thrown horizontally from a point 100 m above the ground with a speed of 20 m/s. Find the time it takes to reach the ground .
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Solution
Given:
Speed of the ball, ux = 20 m/s
Height from which the ball is dropped, h = 100 m
Let t be the time taken by the ball to reach the ground.
Using the equation of motion, we have:
\[h = u_y t + \frac{1}{2}g t^2\]
Here,
Acceleration of gravity, g = 9.8 ms−2
Vertical component of velocity, uy = 0
\[\therefore t = \sqrt{\left( \frac{2h}{g} \right)}\]
\[ \Rightarrow t = \sqrt{\frac{2 \times 100}{9 . 8}} = 4 . 5 s\]
Therefore, the time required by the ball to reach the ground is 4.5 seconds.
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