Question

A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h=-16t^2+120t+10. How long does it take to reach maximum height? What is the boulder's maximum height? round to the nearest hundredth, if neccessary.

Answer 1

\[h=-16t^2+120t+10\]

Answer 2

well we need to know what time t is when the boulder is at max height.

we are given
a=-9.80m/s^2 (this is gravity)
v=120ft/s (we should convert this to m/s or you could convert gravity to ft/s)

and we know that the boulder will reach its max height when v=0

so what equation could you use that would allow us to solve for t?

Answer 3

Actually, they say that the function has height in feet and time in seconds so we should use 32.17 ft/s for gravity

Answer 4

I honestly have no clue, sorry.

Answer 5

well what kinematic equations do you know?

Answer 6

I don't even know what you mean by kinematic, this is my final's review test, I may have been absent when we did this.

Answer 7

Well kinematics allows us to predict an objects motion when acceleration is constant. So when you throw an object up into the air or maybe you throw it to someone else, the only acceleration acting on that object is GRAVITY which is constant.

We are given initial velocity, final velocity and a constant acceleration. We want to find the time t it takes for the boulder to reach its maximum height.

Looking at the function that you posted, we can either find the max height and plug it into that function, or find the time to reach the max height and then plug it into that function.

Answer 8

this site shows the kinematic equations that you need: http://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic-Equations

Answer 9

Thanks

Answer 10

so we see that Vf=Vi+at

we know Vf, Vi, and a which means that we can solve for t.

Then we can plug t into the function they give you in the question to solve for h.

Answer 11

what is the answer?