To determine the initial velocity at which the ball was thrown, we need some additional information. Specifically, we need to know the time it took for the ball to reach the height of 90 meters or any other relevant details such as the angle of projection or the acceleration due to gravity.
If we assume that the ball was thrown vertically upward and neglect air resistance, we can use the equation for the vertical motion of a projectile:
v^2 = u^2 + 2as
where: v = final velocity (0 m/s when the ball reaches its peak) u = initial velocity (the velocity at which the ball was thrown) a = acceleration due to gravity (-9.8 m/s^2, assuming downward as the positive direction) s = displacement (height reached, 90 meters)
Plugging in the known values into the equation, we can solve for the initial velocity (u):
0^2 = u^2 + 2(-9.8)(90)
0 = u^2 - 1764
u^2 = 1764
Taking the square root of both sides:
u ≈ ± 42 m/s
Since the velocity is a vector quantity with both magnitude and direction, we have two possible solutions: one positive and one negative. The positive value indicates that the ball was thrown upward, while the negative value indicates that it was thrown downward.
Therefore, the velocity at which the ball was thrown can be approximately ±42 m/s, depending on the direction (upward or downward) of the throw.