This is the only problem on my homework I don't get, can someone help me out in any way possible? Thanks :)
The blue point begins at (0,80) moving straight downward at 4 unit/sec. The red begins at (70,0) moving 8 unit/sec at 160 degrees. Create the equations that model this.
x(t)=
y(t)=
x(t)=
y(t)=
The blue point begins at (0,80) moving straight downward at 4 unit/sec. The red begins at (70,0) moving 8 unit/sec at 160 degrees. Create the equations that model this.
x(t)=
y(t)=
x(t)=
y(t)=
-
Blue Point (simple):
x(t) = 0, because the x value doesnt change at all throughout time
y(t) = -4t + 80 = 20 - t, because it starts from 80 and moves downwards 4 units/sec
Red Point (more thinking):
x(t) = ?
y(t) = ?
Imagine this drawn in an x-y coordinate.
If the angle is 160 degrees, that means that the other angle is 20 degrees from the y-axis. Across from the 20 degrees is a 90 degree angle if you drew a line from the y-axis to the line that represents the direction of the red point.
The distance from the point (70,0) to the vertical line is trX(t), and the distance from the y-axis to the direction-line is trY(t).
Note: trX and trY are the distances based off the triangles, not the actual coordinates
After labeling, you should see a triangle. where the hypotenuse is 8t.
Remembering SohCahToa,
Sin(20) = op/hyp = trY / 8t --> trY = 8t * Sin(20degrees)
Cos(20) = adj/hyp = trX / 8t --> trX = 8t * Cos(20degrees)
Now we have the distances figured out, we need to figure out the exact coordinates on the graph:
y(t) = trY(t) because the starting point for the red point is y = 0
x(t) = 70 - trX(t) because it starts at x=70 and moves towards the left.
Therefore, for the Red Point:
x(t) = 70 - 8t*Cos(20degrees)
y(t) = 8t*Sin(20degrees)
x(t) = 0, because the x value doesnt change at all throughout time
y(t) = -4t + 80 = 20 - t, because it starts from 80 and moves downwards 4 units/sec
Red Point (more thinking):
x(t) = ?
y(t) = ?
Imagine this drawn in an x-y coordinate.
If the angle is 160 degrees, that means that the other angle is 20 degrees from the y-axis. Across from the 20 degrees is a 90 degree angle if you drew a line from the y-axis to the line that represents the direction of the red point.
The distance from the point (70,0) to the vertical line is trX(t), and the distance from the y-axis to the direction-line is trY(t).
Note: trX and trY are the distances based off the triangles, not the actual coordinates
After labeling, you should see a triangle. where the hypotenuse is 8t.
Remembering SohCahToa,
Sin(20) = op/hyp = trY / 8t --> trY = 8t * Sin(20degrees)
Cos(20) = adj/hyp = trX / 8t --> trX = 8t * Cos(20degrees)
Now we have the distances figured out, we need to figure out the exact coordinates on the graph:
y(t) = trY(t) because the starting point for the red point is y = 0
x(t) = 70 - trX(t) because it starts at x=70 and moves towards the left.
Therefore, for the Red Point:
x(t) = 70 - 8t*Cos(20degrees)
y(t) = 8t*Sin(20degrees)
-
Blue point:
x(t) = 0 [because x doesn't change]
y(t) = -4t + 80 = -t + 20 [because you start at y = 80]
Red point:
x(t) = -8t(cos 20) + 70 [because you start at x = 70, and your angle is 160 (180-160 = 20) so it's negative movement]
y(t) = 8t(sin 20) [because you start at y=0, and your angle is 160 (180-160 = 20) so it's positive movement]
x(t) = 0 [because x doesn't change]
y(t) = -4t + 80 = -t + 20 [because you start at y = 80]
Red point:
x(t) = -8t(cos 20) + 70 [because you start at x = 70, and your angle is 160 (180-160 = 20) so it's negative movement]
y(t) = 8t(sin 20) [because you start at y=0, and your angle is 160 (180-160 = 20) so it's positive movement]