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.
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.