Worksheet: Joint Variation

In this worksheet, we will practice writing an equation to describe joint variation and using proportions to find other sets of values to solve real-world problems.


The kinetic energy 𝐾 of a moving object varies jointly with its mass 𝑚 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 1,000 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?

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