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A package is released from an aircraft flying level. Its time of fall is found from:
A$t=\sqrt{\dfrac{2y}{g}}$
B$t=\dfrac{v_0\sin\theta}{g}$
C$t=\dfrac{2v_0}{g}$
D$t=\dfrac{y}{v_0}$
Answer & Solution
Correct answer: A. $t=\sqrt{\dfrac{2y}{g}}$
1. Released from level flight, the package starts with zero vertical velocity, so $\theta=0$.
2. The vertical equation $y=v_0\sin\theta\,t+\tfrac12 gt^2$ therefore reduces to $y=\tfrac12 gt^2$.
3. Rearranging for $t$ gives $t=\sqrt{\dfrac{2y}{g}}$.
4. The formula $t=\dfrac{v_0\sin\theta}{g}$ applies to a projectile launched at an angle, and here it evaluates to zero.
5. Missing that a horizontal projection has $\theta=0$ was the recorded error on this question.
_Source: NECTA ACSEE 2023 Physics 131/1, Question 2: Mechanics (Projectile Motion)_