SOLUTION: A ball is thrown vertically upward from the ground. Its distance in feet from the ground in t seconds is s=-16t+224t. After how many seconds will the ball be 720 feet from the​ g

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A ball is thrown vertically upward from the ground. Its distance in feet from the ground in t seconds is s=-16t+224t. After how many seconds will the ball be 720 feet from the​ g      Log On


   

Question 1158307: A ball is thrown vertically upward from the ground. Its distance in feet from the ground in t seconds is s=-16t+224t. After how many seconds will the ball be 720 feet from the​ ground?
please help!
Found 2 solutions by Boreal, jim_thompson5910:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Note, I am assuming you meant s=-16t^2+224t
720=-16t^2+224t
16t^2-224t+720=0
divide by 16
t^2-14t+45=0
(t-9)(t-5)=0
when t= 5 and 9 seconds
graph%28300%2C300%2C-10%2C12%2C-100%2C1000%2C720%2C-16x%5E2%2B224x%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: Either t = 5 seconds or t = 9 seconds

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Work Shown:

The equation should be
s = -16t^2 + 224t
Note the t^2 term as the first term

Plug in s = 720. Then get everything to one side. Afterward, use the quadratic formula to solve for t.

s = -16t^2 + 224t
720 = -16t^2 + 224t
0 = -16t^2 + 224t - 720
-16t^2 + 224t - 720 = 0

Quadratic Formula: Plug in a = -16, b = 224, c = -720
t+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 or t+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29

t+=+%28-224%2Bsqrt%28%28224%29%5E2-4%28-16%29%28-720%29%29%29%2F%282%28-16%29%29 or t+=+%28-224-sqrt%28%28224%29%5E2-4%28-16%29%28-720%29%29%29%2F%282%28-16%29%29

t+=+%28-224%2Bsqrt%284096%29%29%2F%28-32%29 or t+=+%28-224-sqrt%284096%29%29%2F%28-32%29

t+=+%28-224%2B64%29%2F%28-32%29 or t+=+%28-224-64%29%2F%28-32%29

t+=+%28-160%29%2F%28-32%29 or t+=+%28-288%29%2F%28-32%29

t+=+5 or t+=+9


We get two solutions because the ball goes up, but then comes back down again. At t = 5 seconds, the ball is going up. Then at t = 9 seconds, the ball is coming back down. At each of these time values, the height of the ball is 720 feet.