# A ball is kicked horizontally with a speed of 5.0 ms-1 from the roof of a house 3 m high. When will the ball hit the ground?

Question

A ball is kicked horizontally with a speed of 5.0 ms-1 from the roof of a house 3 m high. When will the ball hit the ground?

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1 year 2021-09-03T04:17:39+00:00 1 Answers 35 views 0

the time taken for the ball to hit the ground is 0.424 s

Explanation:

Given;

velocity of the ball, u = 5 m/s

height of the house which the ball was kicked, h = 3m

Apply kinematic equation;

h = ut + ¹/₂gt²

where;

h is height above ground

u is velocity

g is acceleration due to gravity

t is the time taken for the ball to hit the ground

Substitute the given values and solve for t

3 = 5t + ¹/₂(9.8)t²

3 = 5t + 4.9t²

4.9t² + 5t -3 = 0

a = 4.9, b = 5, c = -3

Solve for t using formula method

$$t = \frac{-5 +/-\sqrt{5^2-4(4.9*-3)}}{2(4.9)} = \frac{-5+/-(9.154)}{9.8} \\\\t = \frac{-5+9.154}{9.8} \ or \ \frac{-5-9.154}{9.8} \\\\t = \frac{4.154}{9.8} \ or \ \frac{-14.154}{9.8} \\\\t = 0.424 \ sec \ or -1.444 \ sec\\\\Thus, t = 0.424 \ sec$$