A toy rocket is launched

Question

A toy rocket is launched from the top of a building 125 feet tall at an initial velocity of 191 feet per second.
a) Give the function that describes the height of the rocket in terms of time t.
b) Determine the time at which the rocket reaches its maximum height, and the maximum height in feet.
c) For what time interval will the rocket be more than 662 feet above ground level?
d) After how many seconds will it hit the ground?

Answer 1

(a)

 

h(t) = -16t² + 191t + 125

 

(b)

 

h_max occurs at the vertex of the height vs. time parabola.

 

t = -191/[2(-16)] = ?

 

h_max = h(t)

 

(c)

 

Set h(t) = 662 and solve for t. 

 

662 = -16t² + 191t + 125

 

0 = -16t² + 191t - 537

 

There will be 2 positive solutions.  The lower solution is the beginning of the time interval above 662 ft, and the higher solution is the end of the time interval above 662 ft.

 

(d)

 

Solve for t in

 

h(t) = 0.

 

There will be a negative and a positive solution.  Discard the negative solution, since time starts at t = 0.