What is the height function?

Question

The height s above the ground at time t of a falling object is given by
s(t) = −5t2 + v0t + s0
where s is in meters, t is in seconds, v0 is the object's initial velocity in meters per second and s0 is its initial position in meters.

 

 What would the height function be if instead of shooting the marble up off of the tower, you were to shoot it straight DOWN with an initial speed of 30 meters per second from the top of the tower 80 meters tall?

Answer 1

If up is positive, down is negative, and the origin is at ground level, replace v₀ with -30 m/s, and set s₀ equal to 80 m.  The -5t² term will not change.

 

s(t) = -5t² - 30t + 80

 

[s in meters, t in seconds]