A 4.2-kg object,initially at rest,"explodes" into three objects of equal mass.Two of these are determined to have velocities of equal magnitudes (5.0 m/s)with directions that differ by 90$\degree$.How much kinetic energy was released in the explosion?
A)70 J
B)53 J
C)60 J
D)64 J
E)35 J

Question

Quizplus · Accepted Answer

The total kinetic energy released in the explosion is equal to the sum of the kinetic energies of the three objects. The kinetic energy of each object is given by:$$KE = 1/2 mv^2$$where m is the mass of the object and v is its velocity.The two objects that have velocities of equal magnitudes have a combined kinetic energy of:$$KE = 1/2 (2m) (5.0 m/s)^2 = 25 J$$The third object has a kinetic energy of:$$KE = 1/2 m (5.0 m/s)^2 = 12.5 J$$Therefore, the total kinetic energy released in the explosion is:$$KE = 25 J + 12.5 J = 37.5 J$$

A 42-Kg Object,initially at Rest,"explodes" into Three Objects of Equal Mass