SOLUTION: A ball is thrown upward from the roof of a 120-ft building with an initial velocity of 20 ft/s. How long does it take the ball to fall back to the ground?

Algebra ->  Expressions-with-variables -> SOLUTION: A ball is thrown upward from the roof of a 120-ft building with an initial velocity of 20 ft/s. How long does it take the ball to fall back to the ground?      Log On


   

Question 112161: A ball is thrown upward from the roof of a 120-ft building with an initial velocity of 20 ft/s. How long does it take the ball to fall back to the ground?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The height of an object propelled upwards from an initial height of h%5B0%5D with an initial velocity of v%5B0%5D is given by the function (height as a function of time):
h%28t%29+=+-16t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D
In your problem:
v%5B0%5D+=+20ft/sec. and
h%5B0%5D+=+120ft.
You want to find out at what time does the height (h) = 0, so, making the appropriate substitutions into the equation, we get:
0+=+-16t%5E2%2B20t%2B120
Using the quadratic formula to solve:
t+=+%28-20%2B-sqrt%2820%5E2-4%28-16%29%28120%29%29%29%2F2%28-16%29 Simplifying this, we get:
t+=+%28-20%2B-sqrt%28400%2B7680%29%29%2F-32
t+=+%28-20%2B-sqrt%288080%29%29%2F-32
t+=+%28-20%2B89.9%29%2F-32 or t+=+%28-20-89.9%29%2F-32
t+=+-2.184 or t+=+3.434
Only the positive value is meaningful here, so the ball reaches the ground in 3.434 seconds.