Question

a ball is dropped from the top of an 75 m building. does it reach the ground within 2.5 s? (hint: see the figure below.)
yes
no
(d = total distance)
(t = 0 v = 0) (0)
(t = 1 s v = 9.8 m/s) (4.90 m)
(t = 2 s v = 19.6 m/s) (19.6 m)
(t = 3 s v = 29.4 m/s) (44.1 m)
(t = 4 s v = 39.2 m/s) (78.4 m)

Explanation:

Step1: Identify the formula for distance in free - fall

The formula for the distance \(d\) fallen by an object in free - fall is \(d = v_0t+\frac{1}{2}gt^{2}\), where \(v_0 = 0\) (initial velocity, since the ball is dropped), and \(g = 9.8\ m/s^{2}\) (acceleration due to gravity). So the formula simplifies to \(d=\frac{1}{2}gt^{2}\).

Step2: Substitute \(t = 2.5\ s\) into the formula

Substitute \(t = 2.5\ s\) and \(g = 9.8\ m/s^{2}\) into \(d=\frac{1}{2}gt^{2}\).

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Answer:

No