At what speed should a vehicle weighing 5 tons move so that it has the same kinetic

At what speed should a vehicle weighing 5 tons move so that it has the same kinetic energy as a projectile weighing 8 kg flying at a speed of 600 m / s?

Initial data: m1 (vehicle weight) = 5 t; m2 (projectile mass) = 8 kg; V (projectile speed) = 600 m / s.

SI system: m1 = 5 t = 5 * 10 ^ 3 kg.

The speed that the car should move can be determined from the equality: Ek1 = Ek2 = 0.5 * m1 * V12 = 0.5 * m2 * V2 ^ 2, whence V1 ^ 2 = m2 * V2 ^ 2 / m1 and V1 = √ (m2 * V2 ^ 2 / m1).

Let’s calculate: V1 = √ (8 * 600 ^ 2 / (5 * 10 ^ 3)) = √576 = 24 m / s.

Answer: The car will have to move at a speed of 24 m / s.