Word Problem Help

[dalasTR]

To estimate th height of a building, a stone is dropped from the top of a building into a pool of water at groud level. How high is the building if the splash is seen 6.8 seconds after the stone is droppped?

I have to use the equation s(t) = -4.9t^2 + v(subscript 0)t + s(subscript 0)

Now the previous question of this series asked that I find the velocity of a projectile shot upward from the surface of the earth with an initial velocity of 120 meters per second, after 5 seconds, and after 10 seconds. My answers were 71 meters/sec and 22 m/sec respectively.
I did this by solving -9.8t + 120

Now, do I find v(6.8) = -9.8t + 120 ???
If so, that is 53.36.....but I highly doubt this is correct because that is the velocity afte 6.8 seconds, not the height of the building. I am stuck with what to do here.

Any help?

 

[mmm4444bot]

I have to use the [height function] s(t) = -4.9t^2 + v[sub:117mjlqp]0[/sub:117mjlqp] + s[sub:117mjlqp]0[/sub:117mjlqp]

Start by understanding the meaning of the two variables and two parameters in this function.

s(t) is the height (in meters) of the stone above the ground at any time t (i.e., t seconds after being released).

v[sub:117mjlqp]0[/sub:117mjlqp] is the initial velocity.

s[sub:117mjlqp]0[/sub:117mjlqp] is the initial height.

We know that the initial velocity is 0 because the stone is simply released (not thrown), at time t = 0.

Therefore, the given function simplifies.

s(t) = -4.9t^2 + s[sub:117mjlqp]0[/sub:117mjlqp]

We also know that s(0) = s[sub:117mjlqp]0[/sub:117mjlqp] because the stone is at its initial height at time t = 0, right?

So, we're looking for the value of s[sub:117mjlqp]0[/sub:117mjlqp] because that's the answer to this exercise.

And, we know that s(6.8) = 0 meters because we're told that the stone hits the water (which, I believe we are to assume, is synonymous with the ground) at time t = 6.8, and the height s(t) obviously equals zero at ground level.

Substitute all of this knowledge into the function.

0 = -4.9(6.8)^2 + s[sub:117mjlqp]0[/sub:117mjlqp]

Solve this equation to find the initial height (i.e, the height of the building).