Can someone answer this

Question

A cannon ball is fired upward with a n initial velocity  of 1000 yards per second from an initial height of 40 feet

1) find the height  s(t) as a function of time t.

2) find the height of the cannon ball 10 seconds after firing 

Answer 1

First, notice that the initial velocity is given in yards per second, while gravitational acceleration is usually expressed in feet per second², and the initial position is given explicitly in feet.  Convert 1000 yd/sec into 3000 ft/sec, so that the units agree.

 

h = -16t² + 3000t + 40

 

h(10) = -16(10)² + 3000(10) + 40

h(10) = -1600 + 30000 + 40 = 28440 ft

Answer 2

Hi Porcia,

 

The general form to find the height as a function of time is:

                 s(t) = s₀ + v₀t - (1/2) g t² 

Where s₀ is the initial height, v₀ is the initial velocity and g is the acceleration of gravity. 

so all you have to do is to plug in the values but making sure that all are in the same units ( ft, second)

 

1) s₀ = 40 ft  g = 32 ft/s²  v₀= 3000 ft/sec  (since 1 yard = 3 ft)

 

          s(t) = -16t² + 3000 t + 40

2) plug in t = 10 seconds 

         s(t)_t=10 =  -16(100) + 3000(10) + 40 = 28440 ft