I’m making an attempt to know the dot product. I’ve discovered a web site that offers you instinct about this matter and one of many examples entails a pace enhance pad:
Think about the pink vector is your pace (x and y course), and the blue vector is the orientation of the enhance pad (x and y course). Bigger numbers are extra energy.
How a lot enhance will you get? For the analogy, think about the pad multiplies your pace:
When you are available in going 0, you may get nothing [if you are just dropped onto the pad, there’s no boost]
When you cross the pad perpendicularly, you may get 0 [just like the banana obliteration, it will give you 0x boost in the perpendicular direction]
However, if we’ve some overlap, our x-speed will get an x-boost, and our y-speed will get a y-boost:
$textual content{Complete} = speed_x cdot boost_x + speed_y cdot boost_y$
Neat, eh? One other technique to see it: your incoming pace is $|a|$, and the max enhance is $|b|$. The proportion of enhance you truly get (primarily based on the way you’re lined up) is $cos(θ)$
, for a complete of $|a| |b|cos(θ)$.
As an instance we’ve an object shifting with a pace v of <3,3> at an angle of 45 levels and a lift pad p of <10,0>. I’m seeking to see the rise of vector v when it hits the pad.
I’ve calculated the dot product acquiring a worth of 30. My questions are:
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how does this worth modify the pace vector?
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And what does this worth truly symbolize? The brand new complete size of v? Does it modify solely the x coordinate of v?
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And the way do I add it over the preliminary vector? What can be the brand new pace vector after the interplay with the enhance pad?
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If we’re to normalize the vectors and calculate the dot product, we get a worth of round 0.70(cos 45). How is that this worth for use on the present pace vector v<3,3>? And what does this proportion symbolize?
Additionally, I think about that the brand new worth for the vector can be only for the body the place it hits the pad, thus to utilize the enhance a timer must be added earlier than the pace comes again to regular.
