What is the relationship between speed and momentum increase?

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The discussion focuses on calculating the speed at which a particle's momentum increases by specific percentages, starting from an initial speed of 0.47c. For a 1% increase, the speed is approximately 0.4747c, but the user struggles with finding the correct speeds for 10% and 100% increases. They initially attempt to apply simple multiplication for these calculations but realize that relativistic effects must be considered. The conversation highlights the importance of understanding the relativistic definition of momentum in these calculations. Ultimately, the user acknowledges a misunderstanding and seeks clarification on the correct approach.
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[SOLVED] Simple Momentum problem

A particle initially has a speed of 0.47c.
(a) At what speed does its momentum increase by 1%?
.4747c
(b) At what speed does its momentum increase by 10%?
____c
(c) At what speed does its momentum increase by 100%?
____c

To get the answer for part a, i just multiplied the speed by 1.01. I assumed that I would do the same, except 1.1 and 2 for parts b and c respectively, but the answers are not right. I have a feeling I'm just missing something but can't quite figure out what it is.
 
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What's the relativistic definition of momentum?
 
ahhh right now i see!
 
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