An object of mass m is dropped at t = 0 from the roof of a building of height h.

Question

An object of mass m is dropped at t = 0 from the roof of a building of height h. While the object is falling, a wind blowing parallel to the face of the building exerts a constant force F on the object. (a) At what time t does the object strike the ground? Express t in terms of g and h. (b) Find an expression in terms of m and F for the acceleration a of the object n the horizontal direction (taken as the positive x direction). (C) How far is the object displaced horizontally before hitting the ground? Answer in terms of m, g, F, and h. (d) Find the magnitude of the object?s acceleration while it is falling, using the variables F, m, and g.

Explanation / Answer

a)

consider the motion along vertical direction

Vi = initial velocity = 0 m/s

Y = displacement = height of building = h

ay = acceleration = g

t = time taken

Using the equation

Y = Vi t + (0.5) ay t2

h = 0 t + (1/2) g t2

t = sqrt (2h/g)

b)

ax = force in X-direction / mass = F/m

c)

consider the motion along vertical direction

Vi = initial velocity = 0 m/s

X = displacement in horizontal direction

ax = acceleration = F/m

t = time taken = sqrt (2h/g)

Using the equation

X = Vi t + (0.5) ax t2

X = 0 t + (1/2) (F/m) (sqrt (2h/g))2

X = (F/2m) (2h/g)

X = Fh/mg

d)

ax = F/m

ay = g

net acceleration : a = sqrt (ax2 + ay2) = sqrt ((F/m)2 + g2)

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