How Do You Calculate Total Displacement in Multi-Directional Vector Problems?

[Marioqwe]

Homework Statement

1.)A car is driven east for a distance of 52 km, then north for 34 km, and then in a direction 35° east of north for 27 km. Draw the vector diagram and determine the total displacement of the car from its starting point.

a. Find the magnitude
b. Find the direction (counter clockwise from east)

The Attempt at a Solution

So I got a. using the unit vector method which gave me 49.49 for the y component, and 74.12 for the x component. The answer for part a is 89.1237 km.

Now, for part b., I'm doing arctan(49.49/74.12) which is equal to 33.73, but it marks me wrong.

Any idea of what's happening?

Homework Statement

2.) Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.50 m due east, then 0.80 m at 22° north of due east. Beetle 2 also makes two runs and the first is 1.6 m at 41° east of due north.

(a) What must be the magnitude of its second run if it is to end up at the new location of beetle 1?

(b) In what direction must it run?

The Attempt at a Solution

For part a., I am assuming that Vector A+Vector B= 0.5 i + 0.8(cos(22) i + sin(22) j) and Vector C= 1.6(cos(41) i + sin(41) j). Vector D would be the magnitude of beetle 2's second run.
So, it'll something like Vector D=Vector A+Vector B-Vector C=(1.24 i +.3 j)-(1.2 i +1.05 j)= .04 i + .75 j

And by using the Pythagorean theorem: .04^2 + .75^2 = .751 and once again, it marks me wrong.

What am I doing wrong?

 

[method_man]

So I got a. using the unit vector method which gave me 49.49 for the y component, and 74.12 for the x component. The answer for part a is 89.1237 km.

Now, for part b., I'm doing arctan(49.49/74.12) which is equal to 33.73, but it marks me wrong.

Any idea of what's happening?


For part a., I am assuming that Vector A+Vector B= 0.5 i + 0.8(cos(22) i + sin(22) j) and Vector C= 1.6(cos(41) i + sin(41) j). Vector D would be the magnitude of beetle 2's second run.
So, it'll something like Vector D=Vector A+Vector B-Vector C=(1.24 i +.3 j)-(1.2 i +1.05 j)= .04 i + .75 j

And by using the Pythagorean theorem: .04^2 + .75^2 = .751 and once again, it marks me wrong.

What am I doing wrong?

For the first one, I think you made the wrong assumption. Same for the C vector in second.
Maybe this could help: http://id.mind.net/~zona/mstm/physics/mechanics/vectors/introduction/introductionVectors.html"

 

[tomcue]

For the first problem, it seems like you have made a mistake in your calculations for the x and y components. The correct values for the x and y components are 49.49 km and 74.12 km, respectively. This gives a total displacement of 89.1237 km, as you have correctly calculated.

For part b, your calculation for the direction is correct. However, it is important to note that the direction should be measured clockwise from the positive x-axis, not counter-clockwise from the east. In this case, the direction would be 56.27 degrees.

For the second problem, your approach is correct. However, your calculation for the magnitude of Vector D seems to be incorrect. The correct value should be 1.24 m, which you have calculated correctly. However, the direction should be measured clockwise from the positive x-axis, not counter-clockwise from the east. In this case, the direction would be 2.70 degrees. This means that the beetle needs to run at a magnitude of 1.24 m at an angle of 2.70 degrees east of north in order to end up at the same location as beetle 1.