Question 110044This question is from textbook university of Phoenix Elementary and Intermediate Algebra
: Ok this is the last problem I will be submitting for a few days. But I'm really having a hard time with it, and thanks in advance for your help. You guys rock!!!!!!!!!!!
If an object is thrown upward, its height h at time t is given by the equation h(t)=-16t^2+Vot+Ho where
Vo=initial velocity
Ho=initial height
Suppose you drop your venti mocha frappuccino with whip from the roller coaster at cedar point amusement park in sandusky, ohio, when you are at its highest point, which is 420 feet above the ground.
a) what is the initial height of the drink? I'm assuming it's 420 ft?
b )what is the initial velocity?
c) write the equation for the height at time t.
d) how long does it take the chai to reach the ground?
This question is from textbook university of Phoenix Elementary and Intermediate Algebra
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! OK this is the last problem I will be submitting for a few days. But I'm really having a
hard time with it, and thanks in advance for your help. You guys rock!!!!!!!!!!!
.
If an object is thrown upward, its height h at time t is given by the equation:
.
h(t)=-16t^2+Vot+Ho
.
where:
.
Vo=initial velocity
Ho=initial height
.
Suppose you drop your venti mocha frappuccino with whip from the roller coaster at Cedar Point
amusement park in Sandusky, Ohio, when you are at the roller coaster's highest point, which
is 420 feet above the ground.
.
a) What is the initial height of the drink?
.
I'm assuming it's 420 ft. <=== Good assumption. Ho = 420 ft.
.
b) What is the initial velocity?
.
At the peak the roller coaster is not going up, and it also is not yet started down. Therefore,
it has no initial velocity, Vo, in the vertical direction. Therefore, Vo = 0
.
c) Write the equation for the height at time t.
.
Start with the given equation:
.
h(t) = -16t^2 + Vot + Ho
.
Then substitute 0 for Vo and 420 for Ho and you get:
.
h(t) = -16t^2 + 0*t + 420
.
and the zero multiplier in the second term cause the second term to drop out. The equation
then becomes:
.
h(t) = -16t^2 + 420
.
This equation is for the height with an initial vertical velocity of zero and an initial height
of 420 feet.
.
d) How long does it take the chai to reach the ground?
.
When the drink reaches the ground its height is zero. Therefore, substitute zero for h(t) and
the equation becomes:
.
0 = -16t^2 + 420
.
Get rid of the -16t^2 on the right side by adding +16t^2 to both sides. With this addition
the equation becomes:
.
16t^2 = 420
.
Divide both sides by 16 and it becomes:
.
t^2 = 420/16 = 26.25
.
Then solve for t by taking the square root of both sides:
.
t = sqrt(26.25) = 5.1235 seconds
.
This means that 5.1235 seconds after the drink falls from the 420 foot height it hits the ground.
.
Hope this helps you to understand the problem.
.
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