Question

A student drops a ball off the top of building and records that the ball takes 2.55s to reach the ground. Determine all unknowns and answer the following questions. Neglect drag.

Answer 1

The unknown variables in the model equation for ball's motion include vertical distance traveled by the ball which is 31.86 m and the final velocity of the ball which is 25 m/s.

The given parameter;

• time of motion of the ball, t = 2.55 s

The equations that model the motion of the ball is given as follows;

$h = v_0_y + \frac{1}{2} gt^2$

$v_f = v_0_y + gt$

All the unknown variables in the equations include;

• $v_0_y$ is the initial vertical velocity of the ball, = 0
• g is the acceleration due to gravity = 9.8 m/s²
• h is the vertical distance traveled by the ball = ?
• $v_f$ is the final velocity of the ball = ?

The vertical distance traveled by the ball is calculated as follows;

$h = \frac{1}{2} gt^2\\\\h = 0.5 \times 9.8 \times 2.55^2\\\\h = 31.86 \ m$

The final velocity of the ball is calculated as follows;

$v_f = 0 + 9.8(2.55)\\\\v_f = 25 \ m/s$

Thus, the unknown variables in the model equation for ball's motion include vertical distance traveled by the ball which is 31.86 m and the final velocity of the ball which is 25 m/s.

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