The kinetic energy of a moving object varies jointly with its mass and the square of its velocity . If an object weighing 40 kilograms with a velocity of 15 meters per second has a kinetic energy of joules, find the kinetic energy if the velocity is increased to 20 meters per second.
The horsepower (hp) that a shaft can safely transmit varies jointly with its speed in revolutions per minute (rpm) and the cube of the diameter. A shaft with a diameter of 3 inches can transmit 45 hp at 100 rpm. What is the diameter of a shaft that can transmit 60 hp at 150 rpm?