A rock is thrown from the top of a 500 foot cliff. After 1 second the rock is traveling 47 feet per second. After 3 seconds the rock is traveling 111 feet per s

Question

Simplify your answer. Use integers or fractions for any numbers in the expression 

 

Answer 1

Revised question:

 

A rock is thrown down from a 500 foot cliff. After 1 second the rock is traveling 47 feet per second. After 3 it is traveling 111 feet per second.

 

A. Assume that the relationship between time, t, and speed, s, is linear and write an equation describing this relationship. Use ordered pairs of the form (t,s).

B. Use this equation to determine the speed of the rock 5 seconds after it was dropped.

 

(A)

 

The correct relation is

 

s(t) = s₀ + at

 

where s(t) = speed at time t in ft/s, s₀ = initial speed in ft/s, a = acceleration in ft/s², t = time in seconds.  Assume DOWN is POSITIVE direction.

 

s(1) = 47 ⇒ 47 = s₀ + a*(1)

 

s(3) = 111 ⇒ 111 = s₀ + a*(3)

 

Solve system of two linear equations in two unknowns s₀ and a:

 

s₀ + a = 47

s₀ + 3a = 111

 

Subtract top equation from bottom equation and get 

 

2a = 64

 

a = 64/2 = 32 ft/s²

 

Plug a = 32 into top equation and get

 

s₀ = 47 - a = 47 - 32 = 15 ft/s

 

Final equation:

 

s(t) = 15 + 32t

 

(B)

 

When t = 5s,

 

s(5) = 15 + 32(5) = 175 ft/s