Answer to Question #169610 in Calculus for Nics

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

Given,

$s= -16t^2\\$

$g= 32ft/sec^2$

$S= 256ft$

(a) Instantaneous velocity of the stone= $g\times t$ ft/sec

So, at t=1sec, the instantaneous velocity of stone = $g\times t=32\times 1=32ft/sec$

(b) Similarly, at t=2sec, the instantaneous velocity of stone =$g\times t_{2sec}=32\times 2= 64 ft/sec$

(c) Total distance travelled to reach the ground $S=\dfrac{1}{2}gt^2$

So, total time it takes to reach ground $t=\sqrt{\dfrac{2S}{g}}=\sqrt{\dfrac{2\times256}{32}}=\sqrt{16}=4 sec$

(d) The stone reaches the ground at t=4sec

So, instantaneous velocity of stone when it reaches ground

$$v= g\times t_{4sec}=32\times 4=128ft/sec$$