Calculus Question

Question

The mad scientist Dr. Experimento has decided to change the strength of gravity so that it will take 1 minute for a stone dropped from rest to fall 10 feet. Assume that the force of gravity gives the stone a constant acceleration a (t) = −G. Find the value of G in feet / sec2 .

Answer 1

The velocity is the integral of the acceleration function.

 

So v(t) = -Gt +c but since we know it is at rest at time 0, we get that c=0 and can write

v(t) = -Gt

 

The position function is the integral of the velocity function, so we get

 

s(t) = -G/2 * t² +c

 

So at time 0, the stone is ten feet above the ground, so we get c=10 and can write

 

s(t) = -G/2 * t² + 10

 

So, note that t is given in seconds, so s(60) =0

 

So -G/2 * 60² + 10 = 0

     -G*1800           = -10

      G                    = 1/180 feet/sec²

 

Hope this helped.