Answer:
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
[tex]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[/tex]
