![]() ![]() ![]() X would be 10 times cosine of this angle. Second nature of how we would figure these things out. The y component of the vector, and it would have Would use a notation, v sub x, and the v sub x would haveīeen this vector right here. I always gave you a vector, like I would drawĪ vector like this. We launch something into- In the projectile motion problems, Both define the same vector, the vector notation is simply cleaner and more easily worked with. this is simpler to work with than the magnitude degree calculation of magnitude is sqrt(5sqrt3^2+10^) and direction is arctan 10/5sqrt3. ![]() Since you already need to break the vectors into components to solve the problem, 5sqrt3 ihat+5 jhat, and 0 ihat+5jhat, you can present the vector as 5sqrt3 ihat+10 jhat. Add a vector with a magnitude 10 at 30 degrees to a vector of magnitude 5 at 90 degrees. It is a shorthand way of writing out the individual components of a vector, which becomes very useful when manipulating multiple vectors. The plus and minus are not operators when you use a comma and parentheses like this, and that is where you need to bring your brain. To visualize what I'm saying, try using a comma in the unit vector notation: (+5) i hat, (-3) j hat. You need to forget about the plus or minus sign as an operator in this and think of it as an indicator of positive or negative values. The i-hat, j-hat, k-hat etc don't just disappear and allow you to add the values to get the magnitude of v. I think what you're missing (it isn't well explained) is that unit vector notation is an alternate way to define a vector, not an actual equation. ![]()
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