Physics: Momentum question in relation to Kinetic Energy?

Question

If you pitch a baseball with twice the kinetic energy you gave it in a previous pitch, the magnitude of its momentum is? I'm looking for how much greater it is, via a factor, such as 2 times greater.

Answer 1

KE = p^2 / 2m

So KE goes like p^2, or p goes like the square root of KE.

So if you double KE, p goes up like sqrt (2)

Answer 2

KE is related to v squared. Momentum is directly related to v. so if KE is doubled, M goes up by sqrt of 2, or 1.4

Answer 3

K.E initial = 0.5 * m * v1* v1

Final K.E = 0.5 * m * v2* v2

K.E Initial/K.E final = 1/2

so, v1^2/v2^2 = 0.5

v2/v1 = 1/0.71 = 1.4

Momentum initial = m*v1
Momentum final = m*v2 = m * 1.4 * v1

So momentum is increased by 1.4 times