   Chapter 3, Problem 36AP

Chapter
Section
Textbook Problem

In a local diner, a customer slides an empty coffee cup down the counter for a refill. The cup slides off the counter and strikes the floor at distance d from the base of the counter. If the height of the counter is h, (a) find an expression for the time t it takes the cup to fall to the floor in terms of the variables h and g. (b) With what speed does the mug leave the counter? Answer in terms of the variables d, g, and h. (c) In the same terms, what is the speed of the cup immediately before it hits the floor? (d) In terms of h and d, what is the direction of the cup’s velocity immediately before it hits the floor?

(a)

To determine
The expression for the time it takes the cup to fall to the floor.

Explanation

When the cup leaves the counter, we can use the kinematic equation

Δy=v0yt+12ayt2

Here,

Δy is the vertical displacement

v0y is the vertical component of the initial velocity

ay is the vertical acceleration

t is the time taken

Substitute h for Δy , 0

(b)

To determine
The speed with which the mug leaves the counter.

(c)

To determine
The speed of the cup immediately before it hits the ground.

(d)

To determine
The direction of cup’s motion before it hits the floor.

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