Story problem

Question

A projectile is launched upward with an initial velocity of 80ft per second from the roof of a building 12ft high. How long will it take until the projectile lands on the ground? Round to nearest hundredth of a second. Use (h(t)=-16tsquared+v0t+s )

Answer 1

h(t) = -16t²+v₀t+h₀

 

Where v₀ is the initial velocity = 80 f/s, and h0 is the initial height = 12 feet

 

h(t) = -16t² + 80t + 12

 

We want h=0, when the projectile hits the ground.

 

0 = -16t² + 80t + 12

 

0 = -4t² + 20t + 3

 

Use the quadratic formula to find t:

 

t = (-20/-8) ± (-1/8)√(20²-4(-4)(3))

 

t = 5/2 ± (1/8)√448 = 5/2 ± √7

 

t ≅ -0.15, 5.15 sec

 

The -0.15 seconds represents the time you would have to have fired the projectile from the ground to reach the 12 foot starting point.  The 5.15 seconds represents the flight time from the 12 foot starting point to reach the ground.

 

Check:

 

h(t) = -16t2+80t+12

h(t=5.15) = -16(5.15²)+80(5.15)+12

h(t=5.15)) = -424 + 412 + 12

h(t=5.15)) = 0