An object of mass m is dropped from the roof of a building of height h. While th

Question

An object of mass m is dropped 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 horizontal force of magnitude F on the object. (a) How long does it take the object to strike the ground? Express the time t in terms of g and h. (b) Find an expression in terms of m and F for the acceleration ax of the object in 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)

here

t = sqrt[2h / g]

b)

a = F/m

c)

Xh = 0.5 * a * t^2 = 0.5 * (F/m) * 2 * g * h = F * g * h / m

d)

a(x) = F / m

a(y) = g

a = sqrt ( a(x)^2 + a(y)^2)

a = sqrt[(F/m)^2 + g^2]

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