If an object is propelled upward fom a height of s feet at an initial velocity of v feet per second, then its height h after t seconds is given by the equation he=−16t squared + vt + s, where h is in feet. If the object is propelled from a height of 44 feet with an initial velocity of 64 feet per second, its height h is given by the equation h=−16t squared + 64t + 4.

Question

If an object is propelled upward fom a height of s feet at an initial velocity of v feet per​ second, then its height h after t seconds is given by the equation he=−16t squared + vt + ​s, where h is in feet. If the object is propelled from a height of 44 feet with an initial velocity of 64 feet per​ second, its height h is given by the equation h=−16t squared + 64t + 4.
After how many seconds is the height 64​feet?

Henry · Answer

S = 44; Not 4.

h = -16t^2 + 64t + 44 = 64.
Divide both sides by 4:
-4t^2 + 16t + 11 = 16,
-4t^2 + 16t -5t = 0,
Use Quadratic Formula:
t = {-16 +- Sqrt(256-80))/-8,
t = (-16 +- 13.3)/-8 = 0.342, and 3.66 Seconds. t = 3.66 seconds.