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 2.0 m/s when the truck is 2.0 m away, what is the speed of the truck relative to the highway?

Answer 1

Answer:

v = 26. 88 m/s +23 m/s

Explanation:

u = 23 m/s, r = 150 cm, u₁ = 2.0 m/s, s =2.0 m

$\frac{1}{s} +\frac{1}{s'} = \frac{2}{R}$

$\frac{1}{2.0 m} +\frac{1}{s'} = \frac{2}{1.50 m}$

Solve s'

$\frac{1}{s'} = \frac{2}{1.50 m} - \frac{1}{2.0 m}$

$\frac{1}{s'} = 1.833 m$

$s' = - 0.545 m$

To determine the speed of the trick to the highway

$\frac{ds}{dt}= \frac{s^2* \frac{ds}{dt}}{s' ^2} =\frac{2.0 ^2m * 2.0 m/s}{0.545^2m}$

$\frac{ds}{dt} = 26.88 m/s$

Now to determine the velocity highway is going to be

v = ds/dt + u

v = 26. 88 m/s +23 m/s