A rocket is traveling at 0.11 c . How fast must itgo in order to QUINTUPLE its m

Question

A rocket is traveling at 0.11c. How fast must itgo in order to QUINTUPLE its momentum?

P = Mo*V/ sq rt ( 1 - V^2/c^2)
P = 1 kg * 0.11 / sq rt (1 - 0.11^2/1^2)
P = 0.11/ sq rt(1 - 0.0121)
P = 0.11 / sq rt (0.9879)
P = 0.11 / 0.993931587
P = 0.110671601 kg*m/s

5 times that

P = 0.553358004 kg*m/s

Plug that in and solve for V

0.553358004 = V/sq rt(1 - V^2/1^2)
0.553358004 = V / sq rt (1 - V^2)
square both sides

0.306205081 = V^2/(1 - V^2)
0.306205081 - 0.306205081 V^2 = V^2

1.306205081 V^2 = 0.306205081
V^2 = 0.2344
V = 0.48 c

0.48/0.11 = 4.40 times faster
A rocket is traveling at 0.11c. How fast must itgo in order to QUINTUPLE its momentum?

P = Mo*V/ sq rt ( 1 - V^2/c^2)
P = 1 kg * 0.11 / sq rt (1 - 0.11^2/1^2)
P = 0.11/ sq rt(1 - 0.0121)
P = 0.11 / sq rt (0.9879)
P = 0.11 / 0.993931587
P = 0.110671601 kg*m/s

5 times that

P = 0.553358004 kg*m/s

Plug that in and solve for V

0.553358004 = V/sq rt(1 - V^2/1^2)
0.553358004 = V / sq rt (1 - V^2)
square both sides

0.306205081 = V^2/(1 - V^2)
0.306205081 - 0.306205081 V^2 = V^2

1.306205081 V^2 = 0.306205081
V^2 = 0.2344
V = 0.48 c

0.48/0.11 = 4.40 times faster

Explanation / Answer

                   [1-(v/c)^2 ] = 1/ 4.0244

                    [1-(v/c)^2 ] = 1/ 16.1959

                         (v/c)^2 = 0.9382

                           (v/c) = 0.9686

                                v= 0.9686c              

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