A cannon fired a shell of mass 16 kilograms at 285 meters per second toward a tank that was moving at 72 kilometers per hour in a straight line directly toward the cannon. Determine the kinetic energy of the shell relative to the motion of the tank.
Let’s begin this question by modeling the situation. We are told that a cannon fires a shell toward a tank that was moving towards it. The shell has a mass of 16 kilograms and is traveling at a velocity of 285 meters per second. The tank is moving in the opposite direction, at a velocity of 72 kilometers per hour. We are interested in the kinetic energy. And we know that this can be calculated using the formula a half 𝑚𝑣 squared, where 𝑚 is the mass and 𝑣 is the velocity. The standard units of mass are kilograms and the standard units of velocity are meters per second. Using these units gives us a kinetic energy in joules.
Our first step is therefore to convert 72 kilometers per hour into meters per second. We know there are 1000 meters in one kilometer and 3600 seconds in one hour. We can therefore multiply 72 by 1000 over 3600. This is the same as dividing 72 by 3.6, giving us an answer of 20. The tank is moving with velocity 20 meters per second toward the cannon.
We are interested in the relative velocity as we want the kinetic energy of the shell relative to the motion of the tank. This can therefore be calculated by subtracting negative 20 from 285. The velocity of the tank is negative 20 as it is moving in the opposite direction to the shell. This is the same as adding 20 to 285, giving us an answer of 305. The relative velocity of the shell to the motion of the tank is 305 meters per second. We can now calculate the kinetic energy by multiplying a half by 16 by 305 squared. This is equal to 744,200.
The kinetic energy of the shell relative to the motion of the tank is 744,200 joules.