Answer:
x=5/4
Explanation:
Since we're finding the time it takes for the ball to reach 25 feet, this means h is 25
h=-16t%5E2%2B40t Start with the given equation
25=-16t%5E2%2B40t Plug in h=25
16t%5E2-40t%2B25=0 Add 16t%5E2 to both sides. Subtract 40t from both sides.
Let's use the quadratic formula to solve for x:
Starting with the general quadratic
ax%5E2%2Bbx%2Bc=0
the general solution using the quadratic equation is:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29
So lets solve 16%2Ax%5E2-40%2Ax%2B25=0 ( notice a=16, b=-40, and c=25)
x+=+%28--40+%2B-+sqrt%28+%28-40%29%5E2-4%2A16%2A25+%29%29%2F%282%2A16%29 Plug in a=16, b=-40, and c=25
x+=+%2840+%2B-+sqrt%28+%28-40%29%5E2-4%2A16%2A25+%29%29%2F%282%2A16%29 Negate -40 to get 40
x+=+%2840+%2B-+sqrt%28+1600-4%2A16%2A25+%29%29%2F%282%2A16%29 Square -40 to get 1600 (note: remember when you square -40, you must square the negative as well. This is because %28-40%29%5E2=-40%2A-40=1600.)
x+=+%2840+%2B-+sqrt%28+1600%2B-1600+%29%29%2F%282%2A16%29 Multiply -4%2A25%2A16 to get -1600
x+=+%2840+%2B-+sqrt%28+0+%29%29%2F%282%2A16%29 Combine like terms in the radicand (everything under the square root)
x+=+%2840+%2B-+0%29%2F%282%2A16%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
x+=+%2840+%2B-+0%29%2F32 Multiply 2 and 16 to get 32
So now the expression breaks down into two parts
x+=+%2840+%2B+0%29%2F32 or x+=+%2840+-+0%29%2F32
Lets look at the first part:
x=%2840+%2B+0%29%2F32
x=40%2F32 Add the terms in the numerator
x=5%2F4 Divide
So one answer is
x=5%2F4
Now lets look at the second part:
x=%2840+-+0%29%2F32
x=40%2F32 Subtract the terms in the numerator
x=5%2F4 Divide
So another answer is
x=5%2F4
So our only solution is:
x=5%2F4 (which is x=1.25 in decimal form)
So at 1.25 seconds, the ball is 25 feet high.