Calculus Problem

Question

A ball is thrown upward from the top of an 80 feet high building with a speed of 64 feet per second. Taking the gravitational acceleration to be 32 feet per second square, write the equation of motion s=f(t) of the ball, taking t=0 to be the time of the release of the ball, and denoting by s the height of the ball above ground level. 

 

 

 

 

Answer 1

s(t) = -16t² +64t + 80

where the first term shows the effect of acceleration downward due to gravity (-½gt²),

the second term shows the distance upward = rate multiplied by time (path would be steady upward, if not for gravity)

and 3rd term is initial displacement up from ground level.