Question

stelano accidentally dropped his sunglasses off the edge of a canyon as he was looking down. the height, ( h(t) ), in meters (as it relates to sea - level), of the sunglasses after ( t ) seconds, is shown in the table.

during its descent, the pair of sunglasses passed by a climber in the canyon 6 seconds after stelano dropped them. to the nearest meter, what is the difference in elevation between stelano and the climber?

height of sunglasses over time

( t )	( h(t) )
1	5.1
2	-9.6
3	-34.1
4	-63.4
5	-112.5
6	-168.4
7	-230.1

240 meters
170 meters
166 meters
230 meters

Explanation:

Step1: Identify initial height

The initial height of the sunglasses when \(t = 0\) is \(h(0)=10\) meters. This represents Stefano's elevation relative to sea - level (since it's the height of the sunglasses when he drops them).

Step2: Identify climber's height

When \(t = 6\) seconds, the height of the sunglasses is \(h(6)=- 166.4\) meters. This is the climber's elevation relative to sea - level.

Step3: Calculate elevation difference

The difference in elevation \(\Delta h\) is given by \(h(0)-h(6)\). So, \(\Delta h=10-(-166.4)=10 + 166.4 = 176.4\approx176\) meters.

Answer:

166 meters