First let's see if it's moving fast enough to be relativistic. Suppose we use the non-relativistic formula p = mv to estimate v. Then v = p/m = (3.71 x 10^-18) / (6.68 x 10^-27) = 5.55 x 10^8, more than the speed of light.
So the non-relativistic formula doesn't work, which means this really is moving at a speed close to that of light and we need the relativistic formula:
p = gamma * mv where gamma = 1/sqrt[1 - (v/c)^2 ]
But since it's relativistic, v is close to c, so p = gamma * mc approximately and gamma = p/mc = (3.71x10^-18) / [ 6.68x10^-27 * 3 x 10^8 ] = 1.85.
Solve for the (v/c) value which gives a gamma of 1.85.
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Verified answer
First let's see if it's moving fast enough to be relativistic. Suppose we use the non-relativistic formula p = mv to estimate v. Then v = p/m = (3.71 x 10^-18) / (6.68 x 10^-27) = 5.55 x 10^8, more than the speed of light.
So the non-relativistic formula doesn't work, which means this really is moving at a speed close to that of light and we need the relativistic formula:
p = gamma * mv where gamma = 1/sqrt[1 - (v/c)^2 ]
But since it's relativistic, v is close to c, so p = gamma * mc approximately and gamma = p/mc = (3.71x10^-18) / [ 6.68x10^-27 * 3 x 10^8 ] = 1.85.
Solve for the (v/c) value which gives a gamma of 1.85.