A ball is thrown upward with a initial velocity of 10m/s . the ball rises and hits the a ceiling 5m high . Determine the time it will take for the ball to reach the ceiling.

Answer 1

To solve this problem, we can use the kinematic equation that relates the height, initial velocity, and time:

h = (vi * t) - (1/2 * g * t^2)

Where:
h = height (5m)
vi = initial velocity (10m/s)
g = acceleration due to gravity (9.8m/s²)
t = time (unknown)

In this case, we are trying to find the time it takes for the ball to reach the ceiling, so we set h = 5m and solve for t.

5 = (10 * t) - (1/2 * 9.8 * t^2)

Rearranging the equation:

0 = 4.9t^2 - 10t + 5

Using the quadratic formula:

t = [-(-10) ± √((-10)^2 - 4 * 4.9 * 5)] / (2 * 4.9)

t = [10 ± √(100 - 98)] / 9.8

t = [10 ± √2] / 9.8

Simplifying further:

t ≈ (10 + √2) / 9.8 ≈ 1.03 seconds (rounded to two decimal places)

Therefore, it will take approximately 1.03 seconds for the ball to reach the ceiling.