If a ball is thrown vertically upward from the roof of a 64 foot building with a velocity of 80 ft/s, it's height after t sexonds is s(t)=64+80t-16t^2. What is the maximum height the ball reaches? What is the velocity of the ball when it hits the ground?
A body is thrown straight up with initial velocity 5 feet per second from a height of 40 feet. After how many seconds will it hit the ground? What will be its maximum height?
since we have our position function , we can differentiate it to find the velocity:
. The projectile is at it's maximum height when . Thus, we see that:
seconds. To find the value of the maximum height, we plug the t value into the position function, s(t).
max height: .
to find the maximum velocity when it strikes the ground, find where and then plug the value into v(t).
when .
We take the positive value and substitute it into velocity:
. The negative tells us its direction (down). It will have a velocity of as it hits the ground.
For the second question, first come up with s(t).
. We know , , and . Our equation now becomes:
.
Why don't you try this one yourself? If you get stuck, I'll be here to help.