Physics

he drawing shows two planes each dropping an empty fuel tank. At the moment of release each plane has the same speed of 185 m/s, and each tank is at the same height of 3.62 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.

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  1. I'll do (a) and (b). The other plane is similar.

    Since the plane is flying at an angle of 15° upward, the tank when released as a velocity of
    185sin15° = 47.88 m/s vertically
    185cos15° = 178.70 m/s horizontally

    How long does it take the tank to hit the ground?

    3620+47.88t-4.9t^2 = 0
    t = 32.50
    So, the vertical speed on impact is
    47.88-32.50*9.8 = -270.62

    Thus, on impact, the speed is
    √(178.70^2 + 270.62^2) = 324.30 m/s
    In a direction θ where
    tanθ = -270.62/178.70 = -56.56°

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