I am having trouble w/ 'A person throws a rock up with....'

[dbob85]

A person is standing at the top of a building and throws a rock with a certain intial velocity (v) upward and observes that it passes him on the way back down at exactly 2 sec. Two seconds later it hits the ground at the base of the building. Determine the height of the building in feet.

I know that h(t) = -(1/2)(32)t^2 + v(t) + s, where s is the height of the building. But I don't know how to plug in the numbers and solve for height of the building.

 

[stapel]

Just work with the basic equation, definitions, and numbers: If the rock returns to the initial height in two seconds then, by symmetry, it was at zero (the rock was at the maximal height) at one second. So:

. . . . .h(0) = s₀

. . . . .v(t) = -32t + v₀

. . . . .v(0) = v₀

. . . . .v(1) = -32(1) + v₀ = 0

. . . . .v₀ = 32

Then:

. . . . .v(t) = -32t + 32

. . . . .h(t) = -16t² + 32t + s₀

You are also given that the rock is on the ground two seconds after passing the top of the building on the way down. Then:

. . . . .h(2) = -64 + 64 + s₀ = s₀

. . . . .h(4) = -256 + 128 + s₀ = 0

Then what is s₀?

Eliz.

 

[TchrWill]

Re: I am having trouble w/ 'A person throws a rock up with..

A person is standing at the top of a building and throws a rock with a certain intial velocity (v) upward and observes that it passes him on the way back down at exactly 2 sec. Two seconds later it hits the ground at the base of the building. Determine the height of the building in feet.

I know that h(t) = -(1/2)(32)t^2 + v(t) + s, where s is the height of the building. But I don't know how to plug in the numbers and solve for height of the building.

Vo = initial velocity
Vf = final velocity
g = 32 fps^2
h = vertical distance

Since it takes 2 seconds to come back past the person, it took 1 second to go up and 1 second to come down to the observor.
From Vf = Vo - gt, going up, 0 = Vo - 32(1) making Vo = 32 fps.
Coming down, Vf = 0 + 32(1) making Vf = 32 fps at 2 seconds.

From h = Vot + gt^2/2, h = 32(2) + 16(2)^2 = 64 + 64 = 128 feet.