Chapter 3: Vectors and Coordinate Systems

II Ruth sets out to visit her friend Ward, who lives north and east of her. She starts by driving east, but after she comes to a detour that takes her south before going east again. She then drives east for and runs out of gas, so Ward flies there in his small plane to get her. What is Ward's displacement vector? Give your answer (a) in component form, using a coordinate system in which the -axis points north, and (b) as a magnitude and direction.

I A cannon tilted upward at${30}^{°}$ fires a cannonball with a speed of $100\text{m}/\text{s}$. What is the component of the cannonball's velocity parallel to the ground?

I You are fixing the root of your house when a hammer breaks loose and slides down. The roof makes an angle of ${35}^{°}$with the horizontal, and the hammer is moving at $4.5\text{m}/\text{s}$when it reaches the edge. What are the horizontal and vertical components of the hammer's velocity just as it leaves the roof?

I Jack and Jill ran up the hill at $3.0\text{m}/\text{s}$. The horizontal component of Jill's velocity vector was $2.5\text{m}/\text{s}$.

a. What was the angle of the hill?

b. What was the vertical component of Jill's velocity?

I A pine cone falls straight down from a pine tree growing on a${20}^{°}$ slope. The pine cone hits the ground with a speed of $10\text{m}/\text{s}$. What is the component of the pine cone's impact velocity (a) parallel to the ground and (b) perpendicular to the ground?

Kami is walking through the airport with her two-wheeled

suitcase. The suitcase handle is tilted 40° from vertical, and

Kami pulls parallel to the handle with a force of 120 N. (Force is

measured in newtons, abbreviated N.) What are the horizontal and

vertical components of her applied force?

Dee is on a swing in the playground. The chains are 2.5 m long, and the tension in each chain is 450 N when Dee is 55 cm above the lowest point of her swing. Tension is a vector directed along the chain, measured in newtons, abbreviated N. What are the horizontal and vertical components of the tension at this point in the swing?

Kami is walking through the airport with her two-wheeled suitcase. The suitcase handle is tilted 40° from vertical, and Kami pulls parallel to the handle with a force of 120 N. (Force is measured in newtons, abbreviated N.) What are the horizontal and vertical components of her applied force?

Your neighbor Paul has rented a truck with a loading ramp. The ramp is tilted upward at 25°, and Paul is pulling a large crate up the ramp with a rope that angles 10° above the ramp. If Paul pulls with a force of 550 N, what are the horizontal and vertical components of his force? (Force is measured in newtons, abbreviated N.)

Tom is climbing a $3.0-\text{m}$-long ladder that leans against a vertical wall, contacting the wall $2.5\text{m}$above the ground. His weight of$680\text{N}$ is a vector pointing vertically downward. (Weight is measured in newtons, abbreviated N.) What are the components of Tom's weight parallel and perpendicular to the ladder?