Answer to Question #169019 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

Solution

Let s(t) = -16t². Then instantaneous velocity at time t is v(t) = s’(t) = -32t.

A. After 1 sec the instantaneous velocity is v(t) = -32 ft/sec. Negative value means that the speed direction is downward.

B. After 2 sec the instantaneous velocity is v(t) = -64 ft/sec. Its direction is downward too.

C. Stone reach the ground at time t from the equation s(t) = -256 => 16t² = 256 => t² = 16 => t = 4 sec.   

D. At time t = 4 sec when the stone reaches the ground its instantaneous velocity is v(4) = -128 ft/sec. Negative value means that the speed direction is downward.