An airplane flies horizontally with a speed of 300 m/s at an altitude of 400 m a

Question

An airplane flies horizontally with a speed of 300 m/s at an altitude of 400 m above level ground. The pilot (gently) releases a bomb so as to hit a target on the ground. To 2 significant figures, at what horizontal distance from the target must the pilot release the bomb and how long does the bomb remain above the ground after release? {g=9.80m/s2} [Hint: Draw a diagram. The initial velocity of the bomb is the same as that of the airplane. Use a constant-acceleration equation for the x and y directions separately. Use one equation to find the time the bomb remains airborne. Use this time in the other equation to find the horizontal distance.]

Explanation / Answer

This problem comes under an example of horizontal projectile motion. Launching speed (v) of the airplane = 300 m/s Horizontal component of the launching speed of the airplane is vox = 300 m/s Vertical component of the launching speed of the airplane is voy = 0 Initial vertical height (yi) of the airplane = 400 m Final vertical height (yf) of the airplane = 0 From the Kinematic equations of motion we have                    yf - yi = (voy)t - (1/2)gt2                      - 400 m = 0 - (1/2)(9.8 m/s2)(t2)                             t = 9.035 s Then the horizontal distance covered by the bomb is                 R = voxt                    = (300 m/s)(9.035 s)                    = 2710.5 m                    = 2.71 km                    = 2.71 km

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