Is it possible for him?

Classical Mechanics Level 1

Arif and Asif are in a field. Arif sends a ball straight upwards at an initial velocity of 19 ms − 1 19 ~\text{ms}^{-1} . At the same time, Asif is trying to catch that ball (before it touches the ground).

Is it possible for Asif to catch that ball?

Details and assumptions:

  • Asif was 34 m 34~ \text m far from Arif. He was running at an constant velocity of 8 ms − 1 8 ~ \text{ms}^{-1} .

  • The acceleration due to gravity is g = 9.8 ms − 2 g = 9.8 ~ \text{ms}^{-2} .

No Yes

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Munem Shahriar
Apr 17, 2018

We know that v = u − g t ⟹ t = u g [ v = 0 ] v =u - gt \implies t = \dfrac ug ~~~~[v = 0]

t = u g = 19 9.8 s \begin{aligned} t & = \dfrac ug \\ &= \dfrac{19}{9.8} ~ s \\ \end{aligned}

So T = 2 t = 2 × 19 9.8 = 38 9.8 = 3.878 s T = 2t = 2 \times \dfrac{19}{9.8} = \dfrac{38}{9.8} = 3.878 ~ s (Almost).

Let's call the time required for Asif to catch the ball t 1 t_1 . Since Asif was running at an constant velocity, we can use d = v t 1 ⟹ t 1 = d v , d = vt_1 \implies t_1 = \dfrac dv, where d d is the distance.

t 1 = d v = 34 8 = 4.25 s \begin{aligned} t_1 & = \dfrac dv \\ & = \dfrac{34}{8} \\ & = 4.25 ~ s \\ \end{aligned}

We get t 1 > T . t_1 > T. So it is not possible for Asif to catch the ball. The ball will fall to the ground before he arrives there.

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