A ball is thrown vertically upward with a speed of 40 m/s. The time ta

A ball is thrown vertically upward with a speed of 40 m/s. The time taken by the ball to reach the maximum height would be approximately

2 s

3 s

4 s

5 s

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Answer is Wrong!

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UPSC NDA-1 – 2022

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The time taken by the ball to reach the maximum height would be approximately 4 s.

When an object is thrown vertically upward, its velocity decreases due to the acceleration due to gravity ($g$) acting downwards. At the maximum height, the velocity of the object momentarily becomes zero. We can use kinematic equations to find the time taken.

Given initial velocity $u = 40$ m/s. At maximum height, final velocity $v = 0$ m/s. The acceleration due to gravity is $a = -g$. Taking $g \approx 10$ m/s² (a common approximation for simplicity), $a = -10$ m/s². Using the kinematic equation $v = u + at$: $0 = 40 + (-10)t$. Solving for $t$: $10t = 40$, so $t = \frac{40}{10} = 4$ s. Using $g \approx 9.8$ m/s² would give a time slightly less than 4s, but 4s is the closest approximation among the options.

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