An airplane must drop a package of supplies so that it hits the ground at a desi
ID: 2288722 • Letter: A
Question
An airplane must drop a package of supplies so that it hits the ground at a designated spot near some campers. The airplane is moving horizontally with a constant velocity of km/h, approaches the spot at an altitude of 0.500 km above level ground. Having the designated point in sight, the pilot prepares to drop the package.
A) What should the angle between the horizontal and the pilot's line of sigh be when the pack is released?
B) What is the location of the plane when the package hits the ground?
Explanation / Answer
V is the velocity of the plane and ? is the angle of sight of the spot from the horizontal.
The height from the ground is H.
The horizontal distance on the ground of the spot from the vertical from the plane at that instant is S.
Then tan? = H/S--------------(a).
H =g T^2(1/2)
T^2 = 2H/g ------- (b)
S = VT
S^2 = V^2*T^2
S^2 = V^2* (2H/g) from (b)
(H/tan?)^2 = V^2* (2H/g) from (a)
H^2 = V^2* (2H/g) (tan?)^2
(tan?)^2 = gH/ (2 V^2)
g = 9.8 m/s^2, H =500 x10^3 m and V= 38.9 m/s
tan? = 40.24
? = 88.6 degree.
b) Vertically above the spot at an altitude of 500 km.