The driver of a 3000 lb. car, coasting down a hill, sees a red light at the bottom, and must stop. His speed when he applies the brakes is 60 mph, and he is 100 feet (vertically) above the bottom of the hill. (a)How much energy as heat must be dissipated by the brakes if we neglect wind resistance and other frictional effects

Explanation:

60 mph = 60 x 1760 x 3 / (60 x 60) ft /s

speed of car , v = 88 ft /s

kinetic energy of car = 1/2 m v²

= .5 x 3000 x 88²

= 11616 x 10³ poundal - foot

Potential energy = mgh

= 3000 x 32 x 100

=  9600 x 10³ poundal - foot

Total energy = potential energy + kinetic energy

= ( 11616 + 9600 )x 10³

= 21216 x 10³ poundal - foot .

This energy is dissipated as heat when brakes are applied on the car to stop the car .

a

The  winning boat is  boat A

b

Explanation:

From the question we are told that

  The  width of the lake is  

   The  speed of boat A to and fro  is  

   The speed of boat B going is  

    The speed of boat B coming back is  

Generally the time taken by boat A is mathematically represented as

Generally the time taken by boat B is mathematically represented as

The  winning boat is  boat A

The  average velocity is mathematically represented as  

Here d is the total displacement of the winning boat which is  0 m

So