13. 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.

(i) Initial velocity = 49 m/s

Final velocity = 0 m/s

$$a \ = \ g \ = \ –9.8 m/s^2$$

We know that, $$v^2 – u^2 = 2 g s$$ => $$0^2 – (49)^2 = 2 (–9.8) × s$$ => $$s = \frac{49 × 49}{2 × 98} \ => \ s = 122.5 m$$

(ii) We know that, $$v = u + gt$$ => $$0 = 49 + (–9.8) × t$$

∴ $$t = \frac{49}{9.8} \ => \ t = 5 s$$

Total time taken to return the surface of the earth by the ball is 5 s + 5 s = 10 s.