   Chapter 4, Problem 14P

Chapter
Section
Textbook Problem

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 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.

(a)

To determine
The time taken for the object to strike the ground.

Explanation

Given info: The mass of the object is m. The height of the building is h. The horizontal force on the building is F.

When the object is dropped, the force acting on it is the gravity pulling it downwards.

The acceleration along the vertical direction is,

ay=g (I)

• g is the acceleration due to gravity.

The negative sign shows that the force of gravity opposes the direction of motion of the object.

Conclusion:

From Newton’s equations of motion, the formula for the vertical displacement is,

y=viy+12ayt2 (II)

• t is the time taken.
• viy is the y-component of initial velocity.
• y is the total vertical displacement

(b)

To determine
The acceleration along the horizontal direction.

(c)

To determine
The horizontal displacement of the object.

(d)

To determine
The magnitude of the object’s acceleration.

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