SOLUTION: Can someone please help me with this "ballistics word problem? The height of a projectile fired upward with an initial velocity of 400 ft per sec is given by the formula h=-16t^2

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Question 211578This question is from textbook
: Can someone please help me with this "ballistics word problem?
The height of a projectile fired upward with an initial velocity of 400 ft per sec is given by the formula h=-16t^2+400t, where h is the height in ft and t is the time in sec. Find the time required for the projectile to return to earth.
Please show me the steps and please get back before Tues 10am
Thank you so much This question is from textbook

Found 2 solutions by jim_thompson5910, ankor@dixie-net.com:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
h=-16t%5E2%2B400t Start with the given equation.


0=-16t%5E2%2B400t Plug in h=0 (since the ground has a height of 0 ft)


-16t%5E2%2B400t=0 Combine like terms.


Notice that the quadratic -16t%5E2%2B400t%2B0 is in the form of At%5E2%2BBt%2BC where A=-16, B=400, and C=0


Let's use the quadratic formula to solve for "t":


t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


t+=+%28-%28400%29+%2B-+sqrt%28+%28400%29%5E2-4%28-16%29%280%29+%29%29%2F%282%28-16%29%29 Plug in A=-16, B=400, and C=0


t+=+%28-400+%2B-+sqrt%28+160000-4%28-16%29%280%29+%29%29%2F%282%28-16%29%29 Square 400 to get 160000.


t+=+%28-400+%2B-+sqrt%28+160000-0+%29%29%2F%282%28-16%29%29 Multiply 4%28-16%29%280%29 to get 0


t+=+%28-400+%2B-+sqrt%28+160000+%29%29%2F%282%28-16%29%29 Subtract 0 from 160000 to get 160000


t+=+%28-400+%2B-+sqrt%28+160000+%29%29%2F%28-32%29 Multiply 2 and -16 to get -32.


t+=+%28-400+%2B-+400%29%2F%28-32%29 Take the square root of 160000 to get 400.


t+=+%28-400+%2B+400%29%2F%28-32%29 or t+=+%28-400+-+400%29%2F%28-32%29 Break up the expression.


t+=+%280%29%2F%28-32%29 or t+=++%28-800%29%2F%28-32%29 Combine like terms.


t+=+0 or t+=+25 Reduce.


So the solutions are t+=+0 or t+=+25


Since we already know that the projectile is on the ground at t=0 seconds, this means that we can ignore this solution.


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Answer:

So the solution is t=25 which means that it will take 25 seconds for the projectile to return to Earth.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The height of a projectile fired upward with an initial velocity of 400 ft per sec is given by the formula h=-16t^2+400t, where h is the height in ft and t is the time in sec. Find the time required for the projectile to return to earth.
:
h = -16t^2 + 400t
When the projectile returns to earth, h = 0, therefore:
-16t^2 + 400t = 0
factor out -16x
-16t(t - 25) = 0
our solution
t = 25 sec to return to earth
:
:
Check solution in original equation
-16(25^2) + 400(25) =
-16(625) + 10000 =
-10000 + 10000 = 0