Casie M.

asked • 09/20/18# A rock is projected directly upward from ground level, and its height as a function of time is h(t)=-60t^2+90t.

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?

More

## 1 Expert Answer

Arturo O. answered • 09/20/18

Tutor

5.0
(66)
Experienced Physics Teacher for Physics Tutoring

h(t) = -16t

^{2}+ 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 = -16t

^{2}+ 90t-16t

^{2}+ 90t - 120 = 0Using 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.

## Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

#### OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

Arturo O.

^{2}should be -16t^{2}.09/20/18