Question

You are in your car driving on a highway at 23 m/s when you glance in the passenger side mirror (a convex mirror with radius of curvature 150 cm) and notice a truck approaching.
If the image of the truck is approaching the vertex of the mirror at a speed of 1.5 m/s when the truck is 2.0 m away, what is the speed of the truck relative to the highway?

Answer 1

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Answer 2

1/u+1/v=2/R ... (1)

differentiating both sides we have(1/u^2)*du/dt=-(1/v^2)*dv/dt

dv/dt=1.5m/s

u=2m

R=1.5m

from (1) we have

v=1/(2/R-1/u)=1/(2/1.5-1/2)=1.2m

so du/dt=u^2/v^2 *(dv/dt)=4*1.5/1.44=4.16 m/s

Answer 3