High School

Consider a baseball that is thrown straight upward from the roof of a 100-meter high building. It hits the street below eight seconds later. Let \( s(t) \) be the distance between the ball and the ground \( t \) seconds after the ball is thrown upward. If we assume the only force acting on the ball is the force of gravity, which of the following describes the initial velocity of the ball?

A. 0 m/s
B. \(-51.7\) m/s
C. 51.7 m/s
D. 26.7 m/s
E. \(-26.7\) m/s

Answer :

An upward initial velocity of 51.7 m/s will result in the ball reaching a maximum height and descending back to the ground in eight seconds, consistent with the given scenario.

To determine the motion of the ball, we can analyze the given set of data options and determine which one is consistent with the scenario described.

Since the ball is thrown straight upward, its initial velocity should be in the upward direction. The initial velocity determines the behavior of the ball's motion.

Given that the ball hits the street below eight seconds later, we can conclude that the total time of flight is eight seconds. During this time, the ball reaches its maximum height and then descends back to the ground.

Based on the options provided, the only consistent answer is:

Initial velocity of the ball: 51.7 m/s (upward)

Therefore, the initial velocity of the ball is 51.7 m/s (upward).

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