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

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 horizontal constant force 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.

t=_______

(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).
ax = _______

(c) How far is the object displaced horizontally before hitting the ground? Answer in terms of m, g, F, and h.
x = __________

(d) Find the magnitude of the object's acceleration while it is falling, using the variables F, m, and g.
a = ____________

Explanation / Answer

a)

along vertical

initial velocity = voy = 0

acceleration ay = -g

displacement = -h

from equations of motion

y = voy*t + 0.5*g*t^2

-h = -0.5*g*t^2

t = sqrt(2h/g)

2)

along horizantal

iniital velocity vox = 0

Fx = F

acceleration = ax = F/m

(c)

dx = vox*t + 0.5*ax*t^2

dx = 0.5*(F/m)*(2h/g)

dx = Fh/mg

(d)

a = sqrt(ax^2+ay^2)

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

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