Explain in paragraph form

Question

show work and analysis

 

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

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

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

Answer 1

These types of problems need some type of model equation. Do we know what a parabolic height function might look like?

 

s(t)=ax^2+bx+c

 

you are given:

1. s(0)=40 ft
2. Initial shot at 1000 yards/sec

 

When you take derivatives of this distance you get rate of speed, then acceleration. Do that first.

 

After taking the derivatives, ask yourself:

what acceleration should be on planet earth (gravity; converted to same units as rest).

For the velocity function: what is the rate of speed?

 

Once you have the model, does it conform to what you expect? If yes, then solve the parts afterwards.. (Careful with the units, I see yards, feet and others)