For Exercises 47-48, a block is attached to a horizontal spring. At time t = 0 , if the block is moving to the left with an initial displacement of 0 ft , a maximum displacement of 1 3 and a frequency of 3 Hz , find a model for the displacement d as a function of time t .
For Exercises 47-48, a block is attached to a horizontal spring. At time t = 0 , if the block is moving to the left with an initial displacement of 0 ft , a maximum displacement of 1 3 and a frequency of 3 Hz , find a model for the displacement d as a function of time t .
Solution Summary: The author explains how to calculate the model for the displacement d as a function of time.
For Exercises 47-48, a block is attached to a horizontal spring.
At time
t
=
0
, if the block is moving to the left with an initial displacement of
0
ft
, a maximum displacement of
1
3
and a frequency of
3
Hz
, find a model for the displacement
d
as a function of time
t
.
A Ferris wheel has a radius of 10 m, and the bottom of the wheel passes 1 m above the ground. If the Ferris wheel makes one complete revolution every 20 s, find an equation that gives the height above the ground of a person on the Ferris wheel as a function of time. (Let y be the height above the ground in meters and let t be the time in seconds. Assume that when t = 0 the person is 11 m above the ground and going up.)
A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 90t, at which time the fuel is exhausted and it becomes a freely "falling" body. Eighteen
seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -11 ft/s in 5 seconds. The rocket then "floats" to the ground at that rate.
(a) Determine the position function s and the velocity function v (for all times t).
4512
if 0 sts 3
405
if 3 26
15r3
if 0 sts 3
405
if 3 26
Thomas' Calculus: Early Transcendentals (14th Edition)
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