I am asking this question for my friend Erin....since she does not have access to a computer. She is a Calculus student.

We saw the question in your database about the velocity of a pendulum swinging.....It is the same exact question....but there is another question......it says....

"estimate the instantaneous rate of change of d with respect to t when t = 1.5. At this time, is the pendulum moving toward or away from the wall? Explain."

we got the rate of change to be approx -31.4159......How do you know which way its moving.

Thanks

Hi Erin,

I agree with your calculations, d'(1.5) = -31.4195 ms/sec.

In the setup of the problem, d(t) is the distance the pendulum is from the wall at t seconds after the start of the motion. Thus d'(t) is the rate at which the distance from the pendulum to the wall is changing t seconds after the start of the motion. Since you found d'(1.5) to be negative the function d(t) is decreasing at t = 1.5 sec. In other words the distance from the pendulum to the wall is decreasing at t = 1.5 sec and thus the pendulum is moving towards the wall.

Harley