Question

A ball is thrown vertically upward with initial velocity v. Find the maximum height H of the ball as a function of v. Then find the initial velocity v required to achieve a height of H.

Answer 1

The maximum height of the ball is where the upwards velocity of the ball = 0. The equation for position as a function of time is H = at^2 + vt + Hinitial. Since you can assume that Hinitial equals zero and that a = -9.8, the function becomes H = -9.8t^2 + vt. Finding v needed to achieve a height of H is just rearranging to equation so that it becomes v = something.

Answer 2

so v= (H +9.8t^2) / t right?

Answer 3

Yes. If you have numbers, all you need to do is plug them in. Otherwise that is your symbolic solution.

Answer 4

but what if i can only use variables that are defined ...so only in terms of h and v

Answer 5

we use an electronic submission that allows for multiple entries..it said this answer was incorrect because t is a variable not defined in this context

Answer 6

If you can't use t, then another way to do this is with energy equations. Kinetic energy at h = 0 must equal the potential energy at h = H. KE = (1/2)mv^2 and PE = mgh. Setting those equal to each other gives:

(1/2)mv^2 = mgh

Cancel out the m

(1/2)v^2 = gh

So h = (v^2)/(2g)

For the second part

(1/2)v^2 = gh

So v^2 = 2gh

Therefore v = sqrt(2gh)

Answer 7

is g -9.8?

Answer 8

No. In this case, since you have to take the square root, g would just be 9.8, otherwise you'd get a complex value.

Answer 9

hm, its still saying this is incorrect