Physics -Vector Problem (angles)?

Question

"While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75.0 m north, 250 m east, 125 m at an angle 30 degrees north of east, and 150 m south. Find the resultant displacement from the cave entrance."

My thoughts on the question so far...I drew it out, and I know that I need to find Ax and Ay for each respective distance via the formulas Ax=cos (theta)r; Ay=sin(theta)r...I then need to add the vectors by separating them into the i & j's...then take the square root of the squares of these components to get the r (displacement) from first to the last point. My biggest problem is figuring out which angle goes with which distance.

Thank you!!

Answer 1

Let north be the positive y direction and east be the positive x direction. The the resultant vector D can be written:

D = i*(250+125*cos(30)) + j*(75+125*sin(30)-150)
where i = unit vector in x and j is unit vector in y

The magnitude (displacement) is

d = sqrt(D "dot" D) = sqrt{[250 + 125*cos(30)]^2 + [75 + 125*sin(30) - 150]^2}

where D "dot" D = dot product (or inner product) of vector D with it self.

Answer 2

You are in the right track...let me give you a few pointers.

Using East displacement as the x vector in the positive direction
North displacement as the y vector in the positive direction
South displacement as the y vector in the negative direction
West displacement as the x vector in the negative direction,

Let's put all terms together

75m N = 75y_hat
250m E = 250x_hat
125m at a 30 deg angle : break this vector into its two components:
x_hat component= 125 cos(30)
y_hat component= 125 sin(30)
150 m South = -150y_hat

Add all x_hat components together, and square this value
Add all y_hat components together and square this value

take the square root of the above sum, and you will get your displacement
the angle is given by arctangent (sum y_hat components/sum of the x_hat components)...be careful to follow the sign conventions.

And that's how is done! Good luck!

Answer 3

Start at E and use vectors as follows:-
EA = (0---75)
AB = (250---0)
BC = 150.cos 30° + i 150.sin 30°
BC = (130---75)
CD = (0-- -150)
Adding vectors gives:-
ED = (380---0)
Resultant displacement = 380 m EAST

Answer 4

hello!
general equation in finding the resultant is R=square root of summation of x^2 and y^2

solution:
summation of x: 250+125co30=258.25
summation of y: 75-150+125sin30= -12.5

x^2=66693.06
y^2=156.25

R=258.55m

angle= arc tan (y/x)
=arc tan -.0484027
i have no calculator here..

Answer 5

hi Antonio, specific you performed interior the dazzling thank you to get the magnitude of the consequent. you opt for the attitude of the consequent 14.00 i -3.00j-6.00k with beneficial Xaxis. this implies the attitude between resultant and that i. bear in mind attitude between 2 vectors A and B is given by capacity of cos @ = A dot B / |A| |B| for this reason on your case cos alpha = 14/15.5 = 0.9032 So required attitude alpha = arc cos (0.9032) = 25.4°(almost)