# I am sure this is easy but i am stuck

• Vane9488
In summary: O = b/a).In summary, the displacement of a grasshopper making four jumps is calculated by adding the x and y components of each jump together. The resulting values, when plugged into the pythagorean theorem and trigonometry equations, give a resultant displacement of 46.97 cm at a direction of 166.97o S of W. It is important to carefully consider the negative signs of each component to accurately determine the magnitude and direction of the resultant displacement.
Vane9488
The question: A grasshopper makes four jumps. The displacement vectors are (1) 27.0 cm due west (2) 23.0 cm, 35.0$$^{o}$$ due south of west (3) 28.0 cm, 55.0$$^{o}$$ south of east and (4) 35.0 cm, 63.0 $$^{o}$$ north of east. Find the magnitude and direction of the resultant displacement. Express the direction with respect to due west.

Vector magnitude direction x component y component
(1) 27.0 cm 0 $$^{o}$$ 27 cos 0$$^{o}$$ 27 sin 0$$^{o}$$
(2) 23.0 cm 35.0 $$^{o}$$ 23 cos 35$$^{o}$$ 23 sin 35$$^{o}$$
(3) 28.0 cm 55.0 $$^{o}$$ 28 cos 55$$^{o}$$ 28 sin 55$$^{o}$$
(4) 35.0 cm 63.0 $$^{o}$$ 35 cos 63$$^{o}$$ 35 sin 63$$^{o}$$

r= resultant variable

I add all of the x components and I get 62 cm.
I add all of the y components and I get 49.5 cm.

r=$$\sqrt{x^{2}+ y^{2}}$$
r=111.5 cm

the direction i get 38.6$$^{o}$$.

Welcome to PF.

I'm not sure you have properly accounted for the signs of your magnitudes. For instance with positive x East then your west vector would be negative.

LowlyPion said:
Welcome to PF.

I'm not sure you have properly accounted for the signs of your magnitudes. For instance with positive x East then your west vector would be negative.

I am still not getting the right answer with this! I am really confused now!

I haven't done vector addition in a while but here it goes!

I use Dx to label the vectors corresponding to the jumps in sequence. I set up my unit so that west is -x and south is -y which is standard I suppose.

D1 = -27cm (negative because it's going west)

D2x = -13.19cm (you get this by sin(35)*23cm, keep in mind that this is a negative because it's moving westward in the x direction.)
D2y = -18.84cm (Same process of above except cos(35)*23cm)

Now that you got the hang of things I'm going to run down to my solution.

D3x = 16.06cm
D3y = -22.93cm

D4x = 15.89cm
D4y = 31.18cm

Sum of X's = 45.76cm
Sum of Y's = -10.59cm

Make a triangle using those two components and your hypotenuse is the composite vector. 46.97cm 13.03o S of E

Is that correct?

nmacholl said:
I haven't done vector addition in a while but here it goes!

I use Dx to label the vectors corresponding to the jumps in sequence. I set up my unit so that west is -x and south is -y which is standard I suppose.

D1 = -27cm (negative because it's going west)

D2x = -13.19cm (you get this by sin(35)*23cm, keep in mind that this is a negative because it's moving westward in the x direction.)
D2y = -18.84cm (Same process of above except cos(35)*23cm)

Now that you got the hang of things I'm going to run down to my solution.

D3x = 16.06cm
D3y = -22.93cm

D4x = 15.89cm
D4y = 31.18cm

Sum of X's = 45.76cm
Sum of Y's = -10.59cm

Make a triangle using those two components and your hypotenuse is the composite vector. 46.97cm 13.03o S of E

Is that correct?

I don't think so because it asks me to express the direction with respect to due west.

Last edited:
Vane9488 said:
No because it asks me to express the direction with respect to due west.

Well that is actually really simple. 13.03o S of E can be converted to W by simple subtraction. 180o - 13.03o = 166.97o
That is to say the new direction is 166.97o S of W.

I hope this helps.

nmacholl said:
Well that is actually really simple. 13.03o S of E can be converted to W by simple subtraction. 180o - 13.03o = 166.97o
That is to say the new direction is 166.97o S of W.

I hope this helps.

Thank You very much but I am still confused

Solving vectors for me is basically 3 steps.
1. Setup two equations. One that adds together all the x components and one that adds together all the y components. For you problem my equations looked like this:

Xtotal = D1 + D2x + D3x + D4x
Ytotal = D2y + D3y + D4y

I use the subscripts to number each vector, and the x/y's to label the x or y component. Notice that since D1 is completely due west it is only present in the x equation because it has no y component.

2. Solve for the components. Use trigonometry to draw out each vector and break it into components. Be mindful of the direction of the vector. If it's moving downwards it's y component will have a negative. If it's moving to the right it's x component will have a negative as well.

3. Plug and chug. Plug all your x and y values for D1...D4 into your two equations from step one. This gives you the total displacement in the x and y directions. Using these values (and watching the signs) you can draw a traingle which becomes your composite vector. All you need now are the Pythagorean theorem and an inverse sine or cosine to find the direction.

Hope this clears up my process.

nmacholl said:
I haven't done vector addition in a while but here it goes!

I use Dx to label the vectors corresponding to the jumps in sequence. I set up my unit so that west is -x and south is -y which is standard I suppose.

D1 = -27cm (negative because it's going west)

D2x = -13.19cm (you get this by sin(35)*23cm, keep in mind that this is a negative because it's moving westward in the x direction.)
D2y = -18.84cm (Same process of above except cos(35)*23cm)

Now that you got the hang of things I'm going to run down to my solution.

D3x = 16.06cm
D3y = -22.93cm

D4x = 15.89cm
D4y = 31.18cm

Sum of X's = 45.76cm
Sum of Y's = -10.59cm

Make a triangle using those two components and your hypotenuse is the composite vector. 46.97cm 13.03o S of E

Is that correct?

Sorry. I think you got your x,y and sin,cos reversed.

Otherwise it looks ok ... except for the result.

LowlyPion said:
Sorry. I think you got your x,y and sin,cos reversed.

Otherwise it looks ok ... except for the result.

You're right I did flip those.
For my new sums I get 23.79 for x and -4.94 for y.
24.29cm @ 11.64o S of E or 168.36o S of W

I think that's better.

I didn't run the numbers.

The OP is encouraged to verify to be certain of the proper magnitude.

mmacholl: That still doesn't look quite right yet. I currently got R = 14.744 cm at 19.589 deg S of W.

## 1. Why am I stuck on something that seems easy?

Stuckness can happen for a variety of reasons, such as lack of understanding, not having the necessary tools or resources, or simply overthinking the problem. It's important to take a step back and assess the situation to figure out the root cause.

## 2. How can I get unstuck?

One approach is to break the problem down into smaller, more manageable parts. This can help you identify where exactly you're stuck and make it easier to find a solution. You can also try seeking help from a colleague or doing some research to gain more insight.

## 3. What if I still can't figure it out?

If you've exhausted all your options and still can't find a solution, it may be helpful to take a break and come back to the problem with a fresh perspective. Sometimes stepping away from a problem can give your brain the space it needs to come up with a solution.

## 4. Is it okay to ask for help?

Absolutely! Asking for help is not a sign of weakness, but rather a sign of actively seeking to improve and learn. Don't hesitate to reach out to a mentor, colleague, or online community for assistance.

## 5. How can I prevent getting stuck in the future?

Reflect on what caused you to get stuck in the first place and try to come up with strategies to avoid it in the future. This could include breaking down problems into smaller parts, building a stronger foundation of knowledge, or seeking help earlier on. Remember that getting stuck is a natural part of the learning process, and with practice, you'll become better at overcoming challenges.

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