Question

The drawing shows two planes each dropping an empty fuel tank. At the moment of release each plane has the same speed of 173 m/s, and each tank is at the same height of 2.75 km above the ground. Although the speeds are the same, the velocities are different at the instant of release, because one plane is flying at an angle of 15.0° above the horizontal and the other is flying at an angle of 15.0° below the horizontal. Find the (a) magnitude and (b) direction of the velocity with which the fuel tank hits the ground if it is from plane A. Find the (c) magnitude and (d) direction of the velocity with which the fuel tank hits the ground if it is from plane B. In each part, give the direction as a positive angle with respect to the horizontal

Answer 1

horizontal speed is the same for both: v_{_x} = 173 cos15°
for each, the height of the tank from dropping is
h(t) = 2750 ± 173sin15° t - 4.9t^2
so, find t when h=0
then the y component is v_{_y} = -9.8t
landing speed is s^2 = v_{_x}^2 + v_{_y}^2
landing angle is tanθ = v_{_y}/v_{_x}

Answer 2

Oops. the y component is v_{_y} = ±173sin15° - 9.8t