An airplane is flying horizontally with a speed of 1000 km/hr (278 m/s) when it drops a payload. The payload hits the ground 37 s later. (Neglect air drag and the curvature of the Earth. Take g = 10 m/s2.)
(a) At what altitude H is the airplane flying?
The speed of the plane does not affect the time to fall. The distance that it falls in time t (when there is no initial vertical velocity component) is
H = (g/2)*t^2
They tell you what to use for g, although it is not the right number.
5m x 37 x 37 = 6845 meters and you should use 4.9 not 5.
H=(10m/s^2)/2 X (37)^2
H=6845m
To find the altitude H at which the airplane is flying, we need to consider the equation of motion for the falling object.
The equation of motion for a falling object without air resistance is given by:
h = ut + (1/2)gt^2
Where:
h is the vertical displacement (altitude)
u is the initial vertical velocity (which is 0 for a dropped object)
t is the time
g is the acceleration due to gravity
In this case, the time taken by the payload to hit the ground is given as 37 seconds and the acceleration due to gravity is given as 10 m/s^2.
Substituting these values into the equation, we get:
h = 0 + (1/2)(10)(37)^2
Calculating the right side of the equation:
h = 0 + (1/2)(10)(1369)
h = 0 + (5)(1369)
h = 6845 meters
Therefore, the altitude at which the airplane is flying is 6845 meters or 6.845 kilometers.