Derivatives ririrnfjf

Question

Consider the position function for free-falling objects.

s(t) = −16t2 + v0t + s0

A ball is thrown straight down from the top of a 485-foot building with an initial velocity of

−20 feet

per second. Give the corresponding position function

s(t).

s(t) =

Correct: Your answer is correct.

Find

s'(t).

s'(t) =

Correct: Your answer is correct.

Give the corresponding velocity function

v(t).

v(t) =

Correct: Your answer is correct.

What is its velocity after 4 seconds?

v(4) =

Correct: Your answer is correct.

ft/s

How many seconds does it take the ball to fall 104 feet?

t =

What is its velocity after falling 104 feet?

v =

Answer 1

s(t)=-16t^2 -20t + 485

s'(t)=v(t) =-32t-20

v(4)=-32(4)-20=-148 feet per second after 4 seconds

s(t)= 485-104 = -16^2-20t +485 = -104

16t^2 +20t -104=0

4t^2 +5t -26 =0

(4t+13)(t-2)=0

t= 2 seconds to fall 104 feet

v(2) = -64-20 = -84 feet per second after 2 seconds