Question

Chapter 03, Problem 23 As preparation for this problem, review Conceptual Example 10. The drawing shows two planes each dropping an empty fuel tank. At the moment of release each plane has the same speed of 123 m/s, and each tank is at the same height of 4.57 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. 15 Fuel tank Plane A 115 Plane B (a) Number (b) Number (c) Number (d) Number Units Units Units Units

Answer 1

Given,

v0 = 123 m/s ; h = 4.57km ; theta = 15 deg

a)for plane A

v0x = 123 cos15 = 118.81 m/s

v0y = 123 sin15 = 31.83 m/s

We know from eqn of motion

v^2 = u^2 + 2 a s

vy = sqrt (v0y^2 - 2 g h)

vy = sqrt (31.83^2 - 2 x 9.8 x -4570) = 301 m/s

v = sqrt (118.81^2 + 301^2) = 323.58 m/s

theta = tan^-1(301/118.81) = 68.46 deg

Hence, v = 323.58 m/s ; theta = 68.46

For plane B

v0x = 123 cos-15 = 118.81 m/s

v0y = 123 sin-15 = -31.83 m/s

since these are same, answer for B will remains same too

Hence, v = 323.58 m/s ; theta = 68.46