Question

A rock is dropped down from the top of a​ 500-foot cliff. After 1​ second, the rock is traveling 32 feet per second. After 5 ​seconds, the rock is traveling 160 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​ (time, speed).
b. Use this equation to determine the speed of the rock 7 seconds after it is dropped.

Answer 1

A) s=32t

B) 224 ft/s

Explanation:

A)

In the form (time, speed), the question gives us the following data: (1,32) and (5,160). Since we are told that the relationship between​ time, t, and​ speed, s, is linear, we know the equation will fit the formula y=mx+c, where m is slope c is the y-intercept and y and x are the co-ordinate values. Plug in (1,32) and (5,160) to find the formula:

y=mx+c

s=mt+c

32=1m+c

c=32-m

160=5m+C

160=5m+32-m

128=4m

m=32

c=32-m

=32-32=0

So our equation is s=32t

B)

s=32t

s=32(7)=224 ft/s