Vector Addition/Components Problem

[Sora03]

Homework Statement

I am having difficulties in analyzing problems. Here are the problems:
A1. A hiker begins trip by walking 25km southeast from her base camp. on the second day, she walks 40km in a direction of 60 degrees N of E, at which point she discovers a forest ranger's tower. Determine the components of the hiker's displacement.
A2. Consider yourself in a car (A) traveling along a straight, level highway with a speed of V(a) = 75km/h. Another car (B) travels at a speed V(b)=90 km/h. Find the differences in the velocities V(ba) = V(b) - V(a) when (a) the car travels in the same direction in front of you and (b) the other car is approaching you traveling the opposite direction,

Homework Equations

Vector Components
sine, cosine, tangent
Pythagorean theorem

The Attempt at a Solution

A1. Given:
A = 25km SE
B = 40km 60 deg NE
∑Fx = -25km + 40km cos60 = -5km
∑Fy = -25km - 40km sin60 = 9.64 km
R=(5^2)+(9.64^2)=10.8 arc tan (y/x) = 62.58deg

other format:
DISTANCE ANGLE x-comp y-comp
25 km - -25km ? -25km? (should this be here or not)
40 km 60 20 km 34.64 km
is my answer right,? do I have to add the 25km as a component for x and y,it does not have any angle but only a direction (SE)

and is the 'Theta' always in the 'x-axis' not in the 'y-axis' also having difficulties in identifying theta.A2. I didn't really understand this problem, how can I use vectors to solve it.?

please help me and thank you

 

[Vagn]

The question implies an angle by telling you that the hiker starts 25km to the southeast. What angle does southeast correspond to from your chose theta axis(look at a compass if you need)?

 

[Sora03]

I think that if there is no angle given It should be 25cos0 = 25km in the x-comp and in the y-comp 0 because 25sin0 = 0? is this true? I don't know about the compass that youre referring to,

 

[Vagn]

Southeast is at a certain angle from north, as shown by a compass, like the one below.

By telling you the hiker walks 25km southeast, the question tells you in what direction she walked and hence you can find an angle from whatever axis you choose to work with.

 

[Sora03]

i don't know if myanswers are correct even if I use the compass, ok i used it but the answer does not make any sense to me?