Final answer:
The initial speed of a ball thrown vertically upwards that takes 8.33s to reach its maximum height can be calculated using kinematic equations. With gravity at -9.8 m/s², the initial speed turns out to be approximately 81.6 m/s.
Step-by-step explanation:
The question involves calculating the initial speed of a ball thrown vertically upwards given the time it takes to reach the maximum height. The motion of the ball is governed by the equations of kinematics under the influence of gravity. We can use the formula v = u + at where v is the final velocity (0 m/s at the maximum height), u is the initial velocity (which we want to find), a is the acceleration due to gravity (-9.8 m/s², it's negative since gravity is acting opposite to the motion), and t is the time (8.33 s).
First, rearrange the formula to solve for u:
u = v - at.
Since the ball stops at its maximum height, v is zero. Plugging in the values we get:
u = 0 - (-9.8 m/s² × 8.33 s),
Which simplifies to:
u = 9.8 m/s² × 8.33 s.
u equals approximately 81.6 m/s.
So, the initial speed of the ball was approximately 81.6 m/s.