SOLUTION: You are hitting baseballs. When tossing the ball into the air, your hand is 5 feet above the ground. You hit the ball when it falls back to a height of 4 feet. If you toss the ba

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Question 1141693: You are hitting baseballs. When tossing the ball into the air, your hand is 5
feet above the ground. You hit the ball when it falls back to a height of 4
feet. If you toss the ball with an initial velocity of 25 feet per second, how
much time will pass before you hit the ball?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
You are hitting baseballs. When tossing the ball into the air, your hand is 5
feet above the ground. You hit the ball when it falls back to a height of 4
feet. If you toss the ball with an initial velocity of 25 feet per second, how
much time will pass before you hit the ball?
The formula for the height above the ground is

h=h%5B0%5D%2Bv%5B0%5D%2At-16t%5E2

where h = final height above ground when time = t.
      ho = initial height above ground = 5 ft
      vo = initial velocity = 25 ft/s.

The two variables are h and t.

We want to find t when h = 4
      
4=5%2B25%2At-16t%5E2

Get in descending order:

16t%5E2-25%2At-1=0

Unfortunately that doesn't factor, so we use the
quadratic formula:

t+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+, a=16, b=-25, c=-1

t+=+%28-%28-25%29+%2B-+sqrt%28+%28-25%29%5E2-4%2816%29%28-1%29+%29%29%2F%282%2816%29%29+

t+=+%2825+%2B-+sqrt%28625%2B64+%29%29%2F32+

t+=+%2825+%2B-+sqrt%28689%29%29%2F32+ 

t=1.601525297 and t=-0.0390252968

We ignore the negative answer.

Answer:  t = 1.6 seconds (rounded to 1 decimal place).

Edwin