Question

An airplane is flying horizontally with a speed of 103 km/hr (278 m/s) when it drops a payload. The payload hits the ground 30 s later. (Neglect air drag and the curvature of the Earth. Take g = 10 m/s².)
At what altitude H is the airplane flying?

Answer 1

Answer:

H = 4500 m

Explanation:

• Once dropped, the payload moves along a trajectory, that can be decomposed along two directions independent each other.
• Just by convenience, we choose these directions to be coincident with the horizontal (-x) and vertical (y) axes.
• As both movements are independent each other due to both are perpendicular, in the vertical direction, the initial speed is 0.
• So, in order  to find the vertical displacement at any point in time, we can use the following kinematic equation, where a=-g., and H = -Δy.

        $H = \frac{1}{2}*g*t^{2} = \frac{1}{2} * 10 m/s2*(30s)^{2} = 4500 m$

• The airpane was flying at a 4500 m altitude.