Time till an object hits the ground

Question

An object is thrown upward from an initial height of h0 meters above the ground at a speed of v0 meters per second. Its height h above the ground after t seconds is given by h(t)=h0+vot-5t^2 .
Write an equation that shows when an object will hit the ground if thrown upward at 8 m/s from a height of 4 m.
Use your equation from part (a) to answer the following questions.
When does the object hit the ground?
At what time does the object reach its maximum height? What is the maximum height?
What is a reasonable domain for the function h(t) ? Explain.

Answer 1

h(t) = -5t² + 8t + 4, h in meters, t in seconds

 

It hits the ground when h(t) = 0

 

-5t² + 8t + 4 = 0

 

Solve for t using the quadratic formula and get t = -0.4 or 2.  Since time must be positive, the answer is

 

t = 2 seconds

 

Maximum height is reached at the vertex of the h(t) parabola.

 

t = -8/[2(-5)] = 0.8 sec

 

h_max = h(0.8) = -5(0.8²) + 8(0.8) + 4 = 7.2 m

 

Domain is from t = 0 to when it hits the ground, since that is the time interval over which h(t) applies.

Domain:  0 ≤ t ≤ 2 sec