Grasshopper's four jumps: finding resultant displacement with vector components

[oreocookie]

1. A grasshopper makes four jumps. THe siplacement vectors are (1) 27 cm, due west; (2) 23 cm, 35 degrees south of west; (3) 28 cm, 55 degrees south of east; and (4) 35 cm, 63 degrees north of east. Find the magnitude and direction of the resultant displacement. Express the direction with respect to due west

Homework Equations

I'm a litle confused with almost everything. I know how to draw the picture though.

The Attempt at a Solution

A= 27 cm
Angle A=180
B=23 cm
Angle B= 35 degres
C= 28 cm
Angle C= 55 degrees
D= 35 cm
Angle D= 63

Ax=Acos0a
= -116.6 cm
Bx=Bcos0b
= -20.8
Cx= -.67 cm
Dx=Dcos0d
=34.5 cm

Ay=Asin0A
= -21.63
By= -9.8 cm
Cy= -27.9 cm
Dy= 5.9 cm

Rx= ax + bx + cx + dx
=Rx= -2.23

Ry= ay+ by + cy + dy
Ry= -53.43 cm

R^2= rx^2 + ry^2
= 53. 48 cm

Angle R= ry/rx
=181.53 degres.

 

[alphysicist]

Hi oreocookie,

1. A grasshopper makes four jumps. THe siplacement vectors are (1) 27 cm, due west; (2) 23 cm, 35 degrees south of west; (3) 28 cm, 55 degrees south of east; and (4) 35 cm, 63 degrees north of east. Find the magnitude and direction of the resultant displacement. Express the direction with respect to due west

Homework Equations

I'm a litle confused with almost everything. I know how to draw the picture though.

The Attempt at a Solution

A= 27 cm
Angle A=180
B=23 cm
Angle B= 35 degres
C= 28 cm
Angle C= 55 degrees
D= 35 cm
Angle D= 63

Ax=Acos0a
= -116.6 cm
Bx=Bcos0b
= -20.8
Cx= -.67 cm
Dx=Dcos0d
=34.5 cm

Ay=Asin0A
= -21.63
By= -9.8 cm
Cy= -27.9 cm
Dy= 5.9 cm

I believe your calculator is set to radians instead of degrees. Try them again (being careful with the signs and the decimal points) and see what you get.

 

[jllorens]

Your method is correct, but if the numbers are wrong, your calculator could indeed be set on the wrong setting. Make sure it is set to "Degrees" and NOT "Radians."

On a TI-83, this can be done by punching the "MODE" button and then selecting "Degrees."