Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time. Clown A has a 40-kg mass; clown B a 60-kg mass. The relation between their kinetic energies at the instant of launch is:
A) $K_{A}=\frac{3}{2} K_{B}$ .
B) $K_{A}=\sqrt{\frac{3}{2}} K_{B}$ .
C)KA = KB.
D) $K_{B}=\sqrt{\frac{3}{2}} K_{A}$ .
E) $K_{B}=\frac{3}{2} K_{A}$ .

Question

Quizplus · Accepted Answer

The kinetic energy of an object is given by the equation KE = (1/2)mv^2, where m is the mass of the object and v is its velocity. Because the two clowns are launched with the spring compressed the same distance, they will have the same velocity when they leave the cannon. Therefore, the kinetic energy of each clown will be directly proportional to its mass. Since clown A has a mass of 40 kg and clown B has a mass of 60 kg, the relation between their kinetic energies at the instant of launch is KA/KB = (1/2)(40)/(1/2)(60) = 2/3. This means that KB is 1.5 times greater than KA. However, the question only asks for the relation between their kinetic energies, not their specific values. The only answer choice that accurately reflects this relationship is C, which states that KA = KB.

Two Clowns Are Launched from the Same Spring-Loaded Circus Cannon KA=32KBK_{A}=\frac{3}{2} K_{B}KA​=23​KB​

Two Clowns Are Launched from the Same Spring-Loaded Circus Cannon $K_{A}=\frac{3}{2} K_{B}$