Algebra word problem

Question

If a projectile is launched from ground level with Vo feet per second, height in feet, t for seconds after launch is given by s=(( -16t^(2) +Vot. Find times that the projectile will reach a)height of 400ft b)return to ground when Vo is 96ft per second

Answer 1

Given:

 

s(t) = -16t² + 96t (initial height is zero)

 

a)  Time to reach 400 ft:

 

s(t) = 400 ft

 

400 = -16t² + 96t

 

-16t² + 96t - 400 = 0

 

Solve this quadratic in t.  You will get two values of t.  One of them will be physically impossible, such as a negative time.  The other time will be the correct solution.

 

b)  Return to ground:

 

s(t) = 0

 

0 = -16t² + 96t

 

Again, solve for t and get two values.  One will be the time when the projectile is launched from the ground.  The other will be the time the projectile returns to the ground, which is what you want.

 

Try working all of this out, and feel free to post a comment if you need additional help.