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, $$T = 2t = 10\ s$$ ScienceNCERTStandard IX

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