A bee flew from a flower located at <-24, -45, 40>m to another flower located at

Question

A bee flew from a flower located at <-24, -45, 40>m to another flower located at <-23, -25, 45>m. What was the bee's displacement from where she started? m

What was the minimum distance the bee traveled? m

The bee then flew to another flower, located at <-92, 29, -44>m. Now, what was the bee's total displacement from where she started? m

What was the minimum total distance the bee traveled? m

If the bee made this entire trip in 2.7 minutes, determine the average speed of the bee, based on the minimum distance it traveled: m/s

Determine the average velocity of the bee: < , , > m/s

Explanation / Answer

by distance formula , distance between points, ( x1,y1,z1) and ( x2,y2,z2) is

d = [ ( x2-x1)2 + (y2-y1)2 + ( z2- z1)2 ] 1/2

1) points are ( -24, -45,40) and ( - 23,-25,45)

displacement = shortest distance between initial and final position

= [ ( -23 + 24)2 + ( -25 + 45)2 + ( 45 - 40)2] 1/2

= 20.639m

2) minimum distance = displacement = 20.639m

3) initial position ( -24,-45,40) , final position ( - 92,29,-44)

displacement = [ ( -92 + 24)2 + ( 29 + 45)2 + ( - 44- 40)2 ] 1/2

= 130.98m

4) total distance bee travelled = distance between points ( -24,-45,40) & ( -23,-25,45) and between points ( -23,-25,45) & ( -92,29,-44)

distance between points ( -23,-25,45) & ( -92,29,-44)is = [ ( -92+ 23)2 + ( 29+25)2 + ( -44-45)2 ] 1/2

   = 124.89m

total distance travelled = 20.639 + 124.89 = 145.53 m

5) time = 2.7 min

average speed = mimimum total distance / time

= 145.53 / 2.7*60

= 0.898 m/s

6) average velocity = displacement / time

= 130.98 / 2.7*60

= 0.8085 m/s

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