On a roller coaster ride the total mass of a cart - with two passengers included - is 319 kg. Peak K is at 43.6 m above the grou
nd and peak L is at 24.4 m. At location K the speed of the cart is 16.4 m/s, and at location L it is 12.4 m/s. (The wheel mechanism on roller coaster carts always keeps the carts safely on the rail.) How much mechanical energy is lost due to friction between the two peaks?
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To convert parametric to Cartesian systems, you need to find a way to get rid of the t's.
In this case, the t's are inside trigonometric functions, so we're going to use a very famous trig identity you should memorize:
If we plug sin(t) and cos(t) into that equation only x and y variables will be left!
BUT there's one thing. The given cos(t + pi/6) has nasty extra stuff in it. However, part a gives you a tip on how to relate x and y to a nice clean cos(t)
So if we do a little rearranging:
Now we can plug these into the famous trig identity!
Do a little bit of adjustments to get that final form asked for, and you'll be able to find those integers of a and b. ;)
In this case, the t's are inside trigonometric functions, so we're going to use a very famous trig identity you should memorize:
If we plug sin(t) and cos(t) into that equation only x and y variables will be left!
BUT there's one thing. The given cos(t + pi/6) has nasty extra stuff in it. However, part a gives you a tip on how to relate x and y to a nice clean cos(t)
So if we do a little rearranging:
Now we can plug these into the famous trig identity!
Do a little bit of adjustments to get that final form asked for, and you'll be able to find those integers of a and b. ;)