Function help?

Question

A water balloon is dropped from the roof of a 60-foot building with an initial velocity of 20
feet per second. The height of the balloon can be modeled by a function.

a. What is tire function that represents the height of the balloon at a specific time? Use
/z(r) to represent the function.
b. How long does it take the balloon to reach the ground? (Round the answer to the
nearest tenth of a second.)
c. What is the balloon's height at t:0.5 seconds'/

Answer 1

a) h = (1/2)gt² + v₀t + h₀

 

Where g = the acceleration due to gravity = -32 ft/s², v₀ = the initial velocity = -20 ft/s, h₀ = the initial height = 60 feet

 

h = -16t² -20t + 60

 

b)  h=0 when the balloon hits the ground, so:

 

0 = -16t² -20t + 60

 

Solve for t (use the quadratic formula)

 

c)  Plug t=0.5 into h = -16t²-20t+60 to get the answer.