Question

The function g(t)=−16t2+vt+h represents the height of an object, g, in feet, above the ground in relation to the time, t, in seconds, since the object was thrown into the air with an initial velocity of v feet per second at an initial height of h feet. A model rocket is launched off the ground at an initial velocity of 80 feet per second. Part A: Write a function that can be used to describe the flight of the model rocket. Part B:What domain makes sense for this function in context?

Answer 1

A) g(t) = - 16*t² + 80*t

B) domain is ( 0 ≤ t ≤ 5 )

Explanation:

A) for the model rocket

h = 0 and v = 80 feet/sec

Then the equation g(t) = -16*t² + v*t + h

became

g(t) = - 16*t² + 80*t + 0 g(t) = - 16*t² + 80*t

B) The equation g(t) = - 16*t² + 80*t is defined for all real numbers then the domain interval for t is ( -∞ , ∞ ). Now in our case, a model rocket was launched is not possible to get negative values for g(t) then the biggest value for t = 5 from

-16*t² + 80*t ≥ 0

-16*t ≥ -80 16*t ≤ 80

t ≤ 5

And the domain is ( 0 ≤ t ≤ 5 )