The relation between kinetic energy
where m is the mass of object
First let momentum is
and Kinetic Energy
Now Kinetic Energy of Body is increased by 100%.
Increase in Kinetic energy
Now the total Kinetic Energy is
Increase in Momentum =
Percent increase in momentum
A 100% increase means that the Kinetic Energy is doubled. The final Kinetic Energy (
Assuming that the mass of the object is unchanged, we can determine the momentum (
The ratio between the final and initial momentum will give us the fractional increase in momentum.
The final momentum will be equal to 1.414 times the initial momentum. In terms of the initial problem statement, this is an increase of about 41.4%.
Notice that if you doubled the mass of the object to increase the Kinetic Energy by a factor of two, the momentum would also double. One assumption you must make with this problem statement is that the mass of the object is unchanged as the kinetic energy is increased. And that's probably the way this question was intended.