Hi Guys!
Need help with this physics problem, I have no idea how to set it up or how to visualize it but would appreciate any help.
Instructions for finding a buried treasure include the following: Go 80 paces at 235°, turn to 130° and walk 115 paces, then travel 100 paces at 157°. Determine the resultant displacement from the starting point.
Thanks in advance!
You can do it on a piece of polar graph paper.
Or, you can break up each vector into N,E components, then add.
N component=Magnitude*cosTheta
E component=Magnitude*sinTheta.
It works every time.
To solve this problem, we need to break down the given instructions and calculate the resultant displacement.
1. Start by visualizing the starting point as the origin (0,0) on a coordinate plane.
2. Go 80 paces at 235° from the starting point. This means you need to move 80 units in the direction of 235°, which is 55° clockwise from the positive x-axis. To find the x and y components of this displacement, we can use trigonometric functions.
The x-component can be found by multiplying the distance (80 paces) by the cosine of the angle (235°):
x1 = 80 * cos(235°)
The y-component can be found by multiplying the distance (80 paces) by the sine of the angle (235°):
y1 = 80 * sin(235°)
3. Turn to 130° and walk 115 paces from the previous position. This means you need to move 115 units in the direction of 130°, which is 40° counterclockwise from the positive x-axis. Again, use trigonometric functions to find the x and y components of this displacement.
The x-component can be found by multiplying the distance (115 paces) by the cosine of the angle (130°):
x2 = 115 * cos(130°)
The y-component can be found by multiplying the distance (115 paces) by the sine of the angle (130°):
y2 = 115 * sin(130°)
4. Finally, travel 100 paces at 157° from the previous position. Follow the same process as before to calculate the x and y components of this displacement using trigonometric functions.
The x-component can be found by multiplying the distance (100 paces) by the cosine of the angle (157°):
x3 = 100 * cos(157°)
The y-component can be found by multiplying the distance (100 paces) by the sine of the angle (157°):
y3 = 100 * sin(157°)
5. To find the resultant displacement, add up the x and y components obtained from each step:
Resultant x-component (Rx) = x1 + x2 + x3
Resultant y-component (Ry) = y1 + y2 + y3
6. To determine the magnitude and direction of the resultant displacement, use the Pythagorean theorem and inverse trigonometric functions:
Resultant magnitude (R) = sqrt(Rx^2 + Ry^2)
Resultant direction = arctan(Ry / Rx)
By following these steps and plugging in the values from each step, you should be able to calculate the resultant displacement from the starting point.