Video Transcript
A body is moving at a constant velocity 𝐯 which is equal to 250𝐢 minus 250𝐣 centimeters per second, where 𝐢 and 𝐣 are two perpendicular unit vectors. Given that the kinetic energy of the body is 4.8 joules, find the mass of the body.
We know that the kinetic energy of any body is equal to a half 𝑚𝑣 squared, where 𝑚 is the mass and 𝑣 the velocity. When the mass is measured in kilograms and the velocity in meters per second, our kinetic energy is in joules. In this question, we are given the kinetic energy in joules; however, we are given the velocity as a vector in centimeters per second.
As there are 100 centimeters in one meter, the velocity vector can be rewritten as 2.5𝐢 minus 2.5𝐣 meters per second. We can find the magnitude of this velocity vector by finding the sum of the squares of the individual components and then square rooting the answer. The magnitude of the velocity is equal to the square root of 2.5 squared plus negative 2.5 squared. This is equal to the square root of 25 over two.
We now have a value of 𝑣 in meters per second and the kinetic energy in joules. Substituting in our values, we have 4.8 is equal to a half multiplied by 𝑚 multiplied by the square root of 25 over two squared. We can multiply both sides of the equation by two so that the left-hand side becomes 9.6. The square root of 25 over two squared is equal to 25 over two. Next, we can divide both sides by 25 over two or 12.5. This gives us a value of 𝑚 equal to 0.768.
The mass of the body is equal to 0.768 kilograms. And as there are 1000 grams in a kilogram, this is equal to 768 grams.
