The left end of a long glass rod 8.40 cm in diameter, with an index of refraction 1.62, is ground and polished to a convex hemispherical surface with a radius of 4.20 cm. An object in the form of an arrow 1.50 mm tall, at right angles to the axis of the rod, is located on the axis 24.0 cm to the left of the vertex of the convex surface. Required:
a. Find the position of the image of the arrow formed by paraxial rays incident on the convex surface.
b. Find the height of the image formed by paraxial rays incident on the convex surface.
c. Is the image erect or inverted?

9 Times

Explanation:

The stopping distance of a car (or any traveling object) is proportional to the square of the speed of the car.

This is a consequence of the work-kinetic energy theorem, which states that the work done on the car is equal to its loss of kinetic energy:

Since the final speed of the car is zero, its final kinetic energy, so we can write:

where

F is the force that stops the car (the force of friction)

d is the stopping distance

m is the mass of the car

v is the initial speed of the car

As we see from the equation, the stopping distance (d) depends on the square of the speed (). Therefore, it the speed is tripled, the stopping distance will acquire a factor , so we will need 9 times the distance to stop.