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Worksheet: Joint Variation

Q1:

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?

Q2:

The kinetic energy 𝐾 of a moving object varies jointly with its mass π‘š and the square of its velocity 𝑣 . If an object weighing 40 kilograms with a velocity of 15 meters per second has a kinetic energy of 1 0 0 0 joules, find the kinetic energy if the velocity is increased to 20 meters per second.