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

H = 4500 m

Step-by-step 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 = (1)/(2)*g*t^(2) = (1)/(2) * 10 m/s2*(30s)^(2) = 4500 m`

• The airpane was flying at a 4500 m altitude.