Question

A rock is dropped from the top of a​ 2000-foot building. After ​second, the rock is traveling feet per second. After ​seconds, the rock is traveling feet per second. Let y be the rate of descent and x be the number of seconds since the rock was dropped. Part A: Write a linear equation that relates time x to rate y. (Hint: Use the ordered pairs (1,32) and (2,64) ) Part B: Use this equation to determine the rate of travel of the rock 17 seconds after it was dropped.

Answer 1

`y = 32x`

The rate is 224 ft/s

Explanation:

Solving (a):

Given

`(x_1,y_1) = (1,32)`

`(x_2,y_2) = (2,64)`

Required

Determine the linear equation

First, we need to determine the slope using

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (64 - 32)/(2 - 1)`

`m = (32)/(1)`

`m = 32`

The equation is then calculated using:

`y - y_1= m(x - x_1)`

`y - 32= 32(x - 1)`

`y - 32= 32x - 32`

Add 32 to both sides

`y - 32 + 32= 32x - 32 + 32`

`y = 32x`

Solving (b):

Given

`x = 7`

Required

Determine y

We have that:

`y = 32x`

Substitute 7 for x

`y=32 * 7`

`y=224`

Hence, the rate is 224 ft/s