A rock is projected directly upward from ground level, and its height as a function of time is h(t)=-60t^2+90t.

Question

a) make a sketch of h(t)

b) Determine the time at which the rock reaches its maximum height, and find that maximum height in feet.

c) For what is the interval will the rock be more than 120 feet above the ground?

d) After how many seconds will the rock hit the ground?

Answer 1

h(t) = -16t² + 90t

 

(a)  This forum does not have graphing capability.

 

(b)

 

Maximum height occurs at the vertex of the height-vs.-time parabola, which is at

 

t = -90/[2(-16)] sec = ? sec

 

Evaluate h(t) at this value of t to get maximum height.

 

(c)

 

Set h(t) = 120, and get a quadratic equation.  Solve the quadratic equation.  The time above 120 is the time interval between the 2 solutions for t.

 

120 = -16t² + 90t

 

-16t² + 90t - 120 = 0

 

Using the quadratic formula, you should get

 

t = 2.17 and 3.45 sec.  So it is above 120 ft between 2.17 and 3.45 sec.

 

(d)

 

Set

 

h(t) = 0

 

and solve the quadratic equation for t.  You will get a negative and a positive solution.  Since time starts at t = 0, the positive solution is the correct answer.