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The x-axis runs along the principal axis of a concave mirror, with the origin at the vertex and the real focus at (6.41 cm,0). The mirror is facing the positive x-axis. A toy car of height 18.5 cm starts at the real focus and moves at constant velocity v = +8.31i cm/s (away from the mirror). Find the rate at which the height of the image size is changing, in cm/s, at the instant the car reaches (91.4 cm,0). The sign will indicate if it the value of the height of the image is increasing or decreasing. HINT: Watch out for signs! Think about the sign of image height!

The x-axis runs along the principal axis of a concave mirror, with the origin at the vertex and the real focus at (6.41 cm,0). The mirror is facing the positive x-axis. A toy car of height 18.5 cm starts at the real focus and moves at constant velocity v = +8.31i cm/s (away from the mirror). Find the rate at which the height of the image size is changing, in cm/s, at the instant the car reaches (91.4 cm,0). The sign will indicate if it the value of the height of the image is increasing or decreasing. HINT: Watch out for signs! Think about the sign of image height!

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The x-axis runs along the principal axis of a concave mirror, with the origin at the vertex and the real focus at (6.41 cm,0). The mirror is facing the positive x-axis. A toy car of height 18.5 cm starts at the real focus and moves at constant velocity v = +8.31i cm/s (away from the mirror). Find the rate at which the height of the image size is changing, in cm/s, at the instant the car reaches (91.4 cm,0). The sign will indicate if it the value of the height of the image is increasing or decreasing. HINT: Watch out for signs! Think about the sign of image height!
Transcribed Image Text:The x-axis runs along the principal axis of a concave mirror, with the origin at the vertex and the real focus at (6.41 cm,0). The mirror is facing the positive x-axis. A toy car of height 18.5 cm starts at the real focus and moves at constant velocity v = +8.31i cm/s (away from the mirror). Find the rate at which the height of the image size is changing, in cm/s, at the instant the car reaches (91.4 cm,0). The sign will indicate if it the value of the height of the image is increasing or decreasing. HINT: Watch out for signs! Think about the sign of image height!
Expert Solution
Step 1

Given,

height of car = 18.5 cm 

iniital object distance = -6.41 cm 

final object distance = -91.4 cm 

focal length = -6.41 cm 

velocity = 8.31 i cm/s

Step 2

Using mirror equation 

for initial condition 

1f=1v+1u-16.41=1v-16.411v=0v=∞then magnificationm=-vum=∞andm=hihohi=∞

Step 3

for final condition

1f=1v+1u-16.41=1v-191.41v=-16.41+191.41v=-91.4+6.416.41*91.4v=-6.893 cmthen magnificationm=-vum=--6.893-91.4m=-0.075andm=hihohi=-0.075*18.5 cmhi=-1.40 cm

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