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A small rocket is launched from a height of 72 feet. The height of the rocket in feet, h, is represented by the equation h(t) = −16t2 + 64t + 72, where t = time, in seconds. Graph this equation on the accompanying grid. Use your graph to determine the number of seconds that the rocket will remain at or above 100 feet from the ground.

A small rocket is launched from a height of
72 feet. The height of the rocket in feet, h, is
represented by the equation
h(t) = −16t2 + 64t + 72, where t = time, in
seconds. Graph this equation on the
accompanying grid. Use your graph to
determine the number of seconds that the
rocket will remain at or above 100 feet from
the ground.

Grade:11

2 Answers

Askiitians Expert Ankit -BVCOE
18 Points
10 years ago

please check the image provided also.

 

When we say 100 feet from ground we should also check that the rocket is already 72 feet above the ground.

so the relative height rocket must reach to attain 100 ft from ground is actually 18 feet.

 

so the equation has been modified to

so now height(h) can be taken as 18 feet.

-16t^2 + 64t +72 >= 18

=> -16t^2 +64t +54 >=0

 which is reduced to  8t^2 -32t -27 >=0

for time > 5 sec this equation is positive .

SO we can say that after time= 5 sec , the rocket will be above 100 feet of height above ground.

PS: there might be some printing error in equation as it is giving only one valid value of time.

 

 

 

 

Bhavesh Pant
18 Points
10 years ago

Sir, you have taken the relative height as 18 feet I think you are incorrect because it must be 28 feet

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