Question

12 at a football game a t - shirt is launched straight up into the air and is in the air for 9.0 s. what will be its maximum height? a 396.9 m b 99.23 m c 9 m d 88.2 m

Explanation:

Step1: Find the time to reach maximum height

The total time of flight \(T = 9.0\ s\). For vertical motion under gravity (symmetric in upward - and downward - motion), the time to reach the maximum height \(t=\frac{T}{2}\).
So, \(t=\frac{9.0}{2}= 4.5\ s\).

Step2: Use the kinematic equation \(h = v_0t-\frac{1}{2}gt^{2}\). At maximum height, the final velocity \(v = v_0 - gt=0\), so \(v_0=gt\). Substituting \(v_0 = gt\) into \(h = v_0t-\frac{1}{2}gt^{2}\), we get \(h=\frac{1}{2}gt^{2}\) (where \(g = 9.8\ m/s^{2}\)).

Substitute \(t = 4.5\ s\) and \(g=9.8\ m/s^{2}\) into the formula \(h=\frac{1}{2}gt^{2}\).
\(h=\frac{1}{2}\times9.8\times(4.5)^{2}\)

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Answer:

B. \(99.23\ m\)