Ruth sets out to visit her friend Ward, who lives 50 mi north and 100 mi east of her. She starts by driving east, but after 60 m

Question

2 years ago

4

Ruth sets out to visit her friend Ward, who lives 50 mi north and 100 mi east of her. She starts by driving east, but after 60 m

i she comes to a detour that takes her 15 mi south before going east again. She then drives east for 8 mi and runs out of gas, so Ward flies there in his small plane to get her.
Part A
What is Ward's displacement vector? Give your answer in component form, using a coordinate system in which the y-axis points north.
Express your answers using two significant figures separated by a comma.
rx,ry = mi
Part B
What is the magnitude of Ward's displacement vector?
Express your answer to two significant figures and include the appropriate units.
Part C
What is the direction of Ward's displacement vector, measured clockwise from the negative y axis?
Express your answer using two significant figures.

Physics

1 answer:

rodikova [14] · Answer 1 · 2023-10-06T14:22:23+03:00

Answer:

A) x = (-32, - 65)

B) 72 miles

C) 26°

Explanation:

A) If we consider Ruth's home as origin, then at wards home, position vector is;

x1 = 100i + 50j

This is because the question said 100miles east of her which is on the positive x-axis and 50 miles north which is on the positive y-axis.

At Ruth's home, position vector will be;

x2 = 68i - 15j

Because she is moving closer to the positive x-axis in 60 miles after which she also flied east in 8 miles. Also, she went south in 15 miles which is down the negative y-axis.

Thus, displacement vector is;

x = x2 - x1 = 68i - 15j - (100i + 50j)

x = 68i - 15j - 100i - 50j

x = -32i - 65j

In component form, we have;

x = (-32, - 65)

B) Magnitude of wards displacement vector;

|x| = √((-32)² + (-65²))

|x| = √(1024 + 4225)

|x| = √5249

|x| ≈ 72 miles

C) direction of Ward's displacement vector, measured clockwise from the negative y axis is;