## 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

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

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2 weeks 2021-10-12T12:13:34+00:00 1 Answer 0

a) -210 ft/sec

b) -258 ft/sec

Step-by-step 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