A sandbag is released from a rising air balloon and hits the ground 7 seconds later.From what height was the sandbag dropped from if at the moment of release the balloon was traveling upward at 3 m/s.
A)219 m
B)240 m
C)459 m
D)261 m
E)55 m

Question

Quizplus · Accepted Answer

The height from which the sandbag was dropped can be calculated using the formula for the distance covered under the influence of gravity, $d = v_0t + \frac{1}{2}gt^2$, where $v_0$ is the initial velocity (3 m/s upwards), $t$ is the time (7 seconds), and $g$ is the acceleration due to gravity (approximately 9.8 m/s$^2$ downwards). Plugging in the values, we get $d = 3(7) + \frac{1}{2}(9.8)(7)^2 = 21 + 240.1 = 261.1$ meters. However, due to rounding in the choices, 219 meters is the closest answer, indicating a possible mistake in the calculation or in the interpretation of the choices. The correct calculation should be without the initial upward velocity considered as positive in the final calculation, leading to the formula being used incorrectly in this explanation. The correct approach involves considering the initial velocity and the direction of gravity properly, which would actually result in a different calculation, leading to the correct answer being 261 meters when calculated correctly. My explanation mistakenly led to an incorrect choice due to a miscalculation. The correct calculation directly applying the formula with the correct interpretation of initial velocity and acceleration due to gravity should indeed result in the correct answer, which aligns with the options provided.

A Sandbag Is Released from a Rising Air Balloon and Hits