Answer to Question #168284 in Calculus for Shein

Question

An object falls from rest, and s =-16t² where s feet is the distance of the object from the starting point at t seconds, and the positive direction is upward. If a stone is dropped from a building 256 ft high, find

A. the instantaneous velocity of the tone 1 sec after it is dropped;

B. the instantaneous velocity of the stone 2 sec after it is dropped;

C. how long it takes the stone to reach the ground;

D. the instantaneous velocity ot the stone when it reaches the ground.

Answer 1

s=-16t² g=32ft/sec²,

a) instantaneos velocit of th stone is v(t)=g*t=32*1=32ft/sec.

b) the same for this case also, v(2)=32*2=64ft/sec.

c)total distance travelled id S=1/2*g*t²=> from tis we can find t=$\sqrt{2S/g}$ =$\sqrt{2*256/32}$ =4 sec.

d) v(4)=g*t=32*4=128ft/sec