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?
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
You are in your car driving on a highway at 23 m/s when you glance in...
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