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Question

A ball is thrown vertically upwards with a velocity of $$49\ m/s$$. Calculate
$$(i)$$ The maximum height to which it rises.
$$(ii)$$ The total time it takes to return to the surface of the earth.


Solution

Given Initial velocity of ball, $$u = 49$$ $$m/s$$
Let the maximum height reached and time taken to reach that height be $$H $$ and $$t$$ respectively.
Assumption: $$g=9.8\ m/s^2$$ holds true (maximum height reached is small compared to the radius of earth)

Velocity of the ball at maximum height is zero, $$v = 0$$

$$v^2 - u^2 = 2a H$$                          
$$0 - (49)^2  = 2 \times (-9.8) \times H$$         
$$\implies  H=  122.5\ m$$               

$$v = u+ at$$
$$0 = 49 - 9.8 t$$            
$$\implies t = 5$$ s
$$\therefore$$ Total time taken by ball to return to the surface, $$T = 2t = 10\ s$$ 

Science
NCERT
Standard IX

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