Vertical Motion of a Ball Thrown Upwards – Rankers Physics
Topic: Kinematics
Subtopic: Motion Under Gravity

Vertical Motion of a Ball Thrown Upwards

A boy is standing on a tower of height \( 60\text{ m}\). With what upward velocity the boy should throw a ball vertically upwards such that the total time of flight of the ball is three times its time of ascent? (\( g = 10\text{ m/s}^2 \))
\( 10\text{ m/s} \)
\( 20\text{ m/s} \)
\( 40\text{ m/s} \)
Not possible

Solution:

Time of ascent is \( t_a = \frac{u}{g} \). The total time of flight is \( T = 3t_a = \frac{3u}{g} \). Using \( s = uT - \frac{1}{2}gT^2 \), we get \( -60 = u\left(\frac{3u}{g}\right) - \frac{1}{2}g\left(\frac{3u}{g}\right)^2 \). Solving this gives \( u = 20\text{ m/s} \).

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