The safety warning label $$Objects in $($the$)$ mirror are closer than they ap$-$ pear$$ printed on the side$-$view mirrors of cars in some countries around the world was popularized in the original Jurassic Park film $(1993).$ In one of the scenes a Tyrannosaurus rex is chasing a jeep with the main characters in it$.$ At one point, the driver of the jeep sees the T$-$Rex in his side$-$view mirror with the darkly humorous warning label printed $($see the image below$).$

$($a$)(5$ points$)$ Is the mirror plane, convex, or concave? For what purpose is this type of mirror chosen?

$($b$)(5$ points$)$ If the radius of curvature of the mirror is $2$ meters and the T$-$Rex got as close as $10$ meters from the mirror and stands $5$ meters tall, how big is the image and how far is it from the mirror?

$($c$)(5$ points$)$ Draw a careful ray diagram indicating the distance s of the object from the mirror, the distance of the image from the mirror s$^(\text{'}),$ the image size y$^(\text{'})$ and the object size y$.$

$($d$)(5$ points$)$ Do your results support or contradict the statement on the warning label? If it contradicts the statement, explain why they say it$.$