Question

When a cricket ball is thrown vertically upwards, it reaches a maximum height of 5 metres.
(a) What was the initial speed of the ball?
(b) How much time is taken by the ball to reach the highest point? (g = 10 m s⁻²)

Answer 1

(a) v (final velocity) = 0 m/s
u (initial velocity) = ?
a (acceleration due to gravity i.e., g) = 10 m/s²
S (distance) = 5 m
υ² − u² = 2aS
(0)² − (u)² = 2 × 10 × 5
−(u)² = 2 × 10 × 5
−(u)² = 100
u = −10 m/s
Answer: u = −10 m/s
Note − The initial velocity was negative i.e. −10 m/s, as it was velocity against gravity because the ball was thrown upwards. This can be neglected.
(b) s (distance) = 5m
u (initial velocity) = 10 m/s
a (acceleration due to gravity i.e., g) = 10m/s²
t (time) = ?
S = ut +1/2 gt²
⇒ 5 = 10 × t + ½ × 10 × t²
⇒ 5 = 10t + 5t²
⇒ t² + 2t − 1 = 0
⇒ t = ($\sqrt{2}$ − 1) s or (−$\sqrt{2}$ − 1) s
Since, time cannot be negative, so, the required answer is ($\sqrt{2}$ − 1) s.