Expert: Paul Klarreich - 10/5/2007

Question
Hi,I really need help for my math homework. Here is the problem.
h(t)= 13sin(4tpi-(pi/2)) + 13
The function above represents the height in inches on a point of the tire as a function of time t(in seconds). The car starts to move at t=o
A. During the first second that the car is moving, at what time t is the point on the tire exactly 13 inches above the ground?
Thanks

Answer
Questioner:   simhadri
Category:  Calculus
Private:  No
 
Subject:  homework help
Question:  Hi,I really need help for my math homework. Here is the problem.
h(t)= 13sin(4tpi-(pi/2)) + 13
The function above represents the height in inches on a point of the tire as a function of time t(in seconds). The car starts to move at t=o
A. During the first second that the car is moving, at what time t is the point on the tire exactly 13 inches above the ground?
Thanks
.........................................
Hi, Simhadri,

If  h(t)= 13 sin(4pi t - pi/2) + 13

[You really should get 16-inch wheels; these 13-inchers are obsolete.]

It seems to me that at t = 0 you have:

h(0) = 13 sin(-pi/2) + 13.
h(0) = 13 (-1) + 13.
h(0) = 0

which means: the point is on the ground, and starting to rotate around the wheel's center.  The point will reach a height of 13 inches when

h(t) = 13 sin(4pi t - pi/2) + 13 = 13, or

13 sin(4pi t - pi/2) = 0

sin(4pi t - pi/2) = 0

which gives:

4pi t - pi/2 = 0

4pi t = pi/2

4t = 1/2

t = 1/8 second.

[At this instant, the tire has rotated 90 degrees from its initial position.]