Question

Math homework that I have no clue how to even approach? Help please.

If a stone is thrown down at 130 ft/s from a height of 1,450 feet, its height after t seconds is given by s = 1,450 − 130t − 16t^2.
(a) Find its average velocity over the period [1, 4].
=___ft/s
(b) Estimate its instantaneous velocity at time t = 4.
=___ ft/s

Answer 1

a) -210 ft/sec

b) -258 ft/sec

Explanation:

given

a) s(t) = - 16t² - 130t + 1450

at t1 = 1:

s(1) = - 16(1)² - 130(1) + 1450

s(1) = - 16 - 130 + 1450

s(1) = 1304

at t2 = 4:

s(2) = - 16(4)² - 130(4) + 1450

s(2) = - 16(16) - 520 + 1450

s(2) = - 256 - 520 + 1450

s(2) = 674

average velocity

Va= [(s(t2) - s(t1)] / (t2 - t1)

⇒ Va= (674-1304)/(4-1)

= -210 ft/sec

the negative sign shows that the ball is moving downward

b) now, instantaneous velocity is give by derivative s'(t) at t

s'(t) = - 32t - 130

t = 4

s'(4) = - 32(4) - 130

s'(4) = - 128 - 130

s'(4) = - 258

therefore instantaneous velocity at t=4 sec

= -258 ft/sec