A ball is thrown straight up and reaches a
maximum height of 7.16 m. What was its initial speed? The acceleration
of gravity is 9.8 m/s
Answer in units of m/s.
To find the initial speed of the ball, we can use the principles of kinematics.
The first step is to determine the time it takes for the ball to reach its maximum height. Since the ball is thrown straight up, it will take the same amount of time to reach the maximum height as it will to fall back down to its starting point.
The formula to find the time taken for the ball to reach maximum height is:
t = sqrt(2h / g)
Where:
h is the maximum height (7.16 m)
g is the acceleration due to gravity (9.8 m/s^2)
Plugging in the values, we get:
t = sqrt(2 * 7.16 / 9.8) ≈ 0.954 s
Now, we can find the initial speed of the ball using the equation for displacement:
h = v0 * t + (1/2) * g * t^2
Where:
v0 is the initial velocity (what we're trying to find)
Rearranging the equation, we get:
v0 = (h - (1/2) * g * t^2) / t
Plugging in the values, we get:
v0 = (7.16 - (1/2) * 9.8 * (0.954)^2) / 0.954 ≈ 4.44 m/s
So, the initial speed of the ball is approximately 4.44 m/s.
Use
v1^2-v0^2 = 2aS
v1=final velocity
v0=initial velocity
a=acceleration
S=distance
Use an appropriate frame of reference such as positive = upwards.