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I was given this following question:
You are on a skateboard moving at 12 m/s [N]. You throw a crumpled piece of paper at 9.0 m/s [N 25 degrees E] at an angle of 35 degrees above the horizontal. The vertical displacement is zero. Where will it land in relation to the starting point?
This one's brutal, and it is required to be answered soon :S
I hope anyone has the "know-how" as to help derive an answer out of this question. Any help is appreciated, and a great thanks in advanced...
If the "thrower" is moving with 12 m/s, so is the thrown piece moving also(before the trow).
If you throw it with 9 m/s, this will add to 12m/s (add the vectors[I don't understand your directions].
Now you have the initial speed and direction of the piece, put in the friction.
To calculate the point where it lands calculate the curve according initial speed, elevation, g-force, direction.
if you have the coordinate axes N-S,E-W,Up-Down, your velocity vectors should be v0=(12,0,0) and (9cos(25)cos(35),9sin(25)cos(35),9sin(35)), gravity a=(0,0,9.8) obviously
ignoring friction the displacement will be v0t+1/2*a*t^2 at any point time t, but you also know that the last displacement cordinate will be 0.
v0=(12,0,0) and (9cos(25)cos(35),9sin(25)cos(35),9sin(35))?
V0 is both of those?
So, how am I supposed to plug this into the equation
d = v0t + 1/2 at^2?
Also, why is time used in this question? Time isn't given, and if I plug what you have given in the equation, we get two unknown variables, and thus cannot solve the displacement. Since the purpose of the question is to find the displacement of the paper from the starting point.
I'm a bit confused at that point. Can you clarify as to how we get the displacement of the crumpled piece of paper on the floor relative to the starting point?
yeah sorry, i was going to write v and v0, just add up those as v0 now, since its relative to the point you were when it was thrown.
time is used in the equation because velocity and acceleration are both timederivatives of displacement. Time isn't given no, but you can solve the equation for (x,y,0), it should give you two t's: 0 - when its thrown, and the t you're looking for, when it lands.