Consumption and Real Estate
A set of supplies of a plane, it falls to earth at some point in the neighborhood are left?
some campers. The plane, moving horizontally at a constant speed of 140 km / h, approaching the city at an altitude of 0500 km on flat terrain. After the notified body is in sight, the pilot prepared to remove the package. (A) What should the angle between the horizontal and the pilot line of sight when the package is released? (B) What is the position of the aircraft when touching the ground?
V is the velocity of the plane and ө 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 tanө = 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/tanө)^2 = V^2* (2H/g) from (a)
H^2 = V^2* (2H/g) (tanө)^2
(tanө)^2 = gH/ (2 V^2)
g = 9.8 m/s^2, H =500 x10^3 m and V= 38.9 m/s
tanө = 40.24
ө = 88.6 degree.
b) Vertically above the spot at an altitude of 500 km.