An airplane is flying at a speed of 200 m/s in level flight at an altitude of 80

Question

An airplane is flying at a speed of 200 m/s in level flight at an altitude of 800 m. A package is
to be dropped from the airplane to land on a target on the ground.
a) At what horizontal distance away from the target should the package be released so that it
lands on the target?
b) What speed will the package have when it hits the ground?
c) In what direction will the package be traveling when it hits the ground?
Problem 2:
A projectile is shot from the edge of a vertical cliff 60.0 m above the ocean. It has a speed of 100
m/s and is fired at an angle of 35.0° above the horizontal.
a) What is the vertical (y) component of its velocity just before hitting the water?
b) At what angle does it hit the water?
c) How long does it spend in the air before hitting the water?
d) How far from the foot of the vertical cliff does the projectile hit the water

Explanation / Answer

Problem 1 In this problem, let's neglect air resistance so that the horizontal component (x-component) of the acceleration of the package is 0. Take upwards as the +y direction. a) Using "s = ut + 0.5at^2", horizontal displacement, x = 200t + 0.5*0t^2 = 200t. Since the package is dropped, the y-component of its velocity starts at 0. y = -800 = 0t + 0.5(-9.8)t^2 = -4.9t^2 t = 12.78s (t>=0) Putting that into the equation for x, horizontal distance = 200*12.78 = 2555.5m b) Use "v = u + at". y-direction: v_y = 0 - 9.8*12.78 = -125.22m/s x-direction: v_x = 200m/s Speed of package = sqrt[(v_x)^2+(v_y)^2] = 235.97m/s c) tan A = v_y/v_x A = -32.05 deg The package will be travelling at a direction 32.05 deg below the horizontal when it hits the ground.

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