The relativistic momentum of an object is given by
[tex]p_r = \gamma m_0 v[/tex]
where
[tex]\gamma= \frac{1}{\sqrt{1- \frac{v^2}{c^2} }} [/tex] is the relativistic factor
[tex]m_0 [/tex] is the rest mass of the object
v is the speed of the object
c is the speed of light
The classical momentum is given by
[tex]p_c = m_0 v[/tex]
The problem says that the ratio between the relativistic and classical momentum of the object is 7.1, so
[tex]7.1 = \frac{p_r}{p_c}= \frac{\gamma m_0 v}{m_0 v} = \gamma [/tex]
Therefore, [tex]\gamma=7.1[/tex], and we can use the definition of [tex]\gamma[/tex] to find the object's speed:
[tex] \frac{1}{ \sqrt{1- \frac{v^2}{c^2} } }=7.1 [/tex]
Solving,
[tex]v= \sqrt{1- \frac{1}{(7.1)^2} } c[/tex]
And by using [tex]c=3 \cdot 10^8 m/s[/tex], we find the velocity of the object:
[tex]v=2.97 \cdot 10^8 m/s[/tex]
