Question

The projectile motion of an object is modeled by the function h (t) = -16t2 + vt + c, where v is the initial velocity of the object, c is the initial height of the object, t represents the time the object is in motion.

The function model can be used to predict the height of an object in motion over time. If the initial velocity of an object is 59 feet per second and the initial height is 6 feet, which function represents the height of the object after t seconds?

Answer 1

The function represents the height of the object after t seconds is

`h(t)=(-16)t^(2) +(59)t +6`

Explanation:

The projectile motion of an object is modeled by the function

`h(t)=(-16)t^(2) +vt +c`

where, v is the initial velocity of the object,

c is the initial height of the object,

t represents the time the object is in motion.

Given that v=59 ft/s and intial height is h(0)=6 ft

h(0)=6 ft

h(0)=
`(-16)(0)^(2) +v(0) +c`

h(0)=c

So, c= 6

Therefore, The function represents the height of the object after t seconds is

`h(t)=(-16)t^(2) +(59)t +6`