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A child drops a ball from a height of 10cm. Assume that its velocity increases uniformly at a rate of 10m/s2. 1- Find the velocity with which the ball strikes the ground and 2- the time taken by the ball to reach the ground.?
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Answer:


Given:

Initial height, h = 10 cm = 0.1 m

Acceleration, a = 10 m/s2

Final velocity, v = ?

Time taken, t = ?


1. Finding final velocity:


Final velocity of the ball can be found by using the formula:

v2 = u2 + 2as


Where,

u = initial velocity = 0

s = distance travelled = h = 0.1 m


Substituting these values in the formula, we get:

v2 = 02 + 2 × 10 × 0.1

v2 = 2

v = √2 ≈ 1.41 m/s


Therefore, the velocity with which the ball strikes the ground is 1.41 m/s.


2. Finding time taken:


The time taken by the ball to reach the ground can be found by using the formula:

s = ut + ½at2


Where,

u = initial velocity = 0

a = acceleration = 10 m/s2

s = distance travelled = h = 0.1 m

t = time taken = ?


Substituting these values in the formula, we get:

0.1 = 0 × t + ½ × 10 × t2

0.1 = 5t2

t2 = 0.02

t = √(0.02) ≈ 0.14 s


Therefore, the time taken by the ball to reach the ground is 0.14 seconds.
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