chapter 3 physics

Vector A has a magnitude of 26 units and points in the positive y-direction. When vector B is added to A, the resultant vector A+B points in the negative y-direction with a magnitude of 15 units. Find the magnitude and direction of B?

An airplane flies 200 km due west from city A to city B and then 285 km in the direction of 29.5 north of west from city B to city C
(a) In straight-line distance, how far is city C from city A
(b) Relative to city A, in what direction is city C?

A force F1 of magnitude 7.00 units acts on an object at the origin in a direction 0=50.0 above the positive x-axis. A second force F2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force F1+F2.

A girl delivering newspapers covers her route by traveling 6.00 blocks west, 4.00 blocks north, and then 2.00 blocks east.
(a) What is her resultant displacement?
(b) What is the total distance she travels?

A vector has an x-component of -26.5 units and a y-component of 31.5 units. Find the magnitude and direction of the vector

A map suggests that Atlanta is 730 miles in a direction 5.00 north of east from Dallas. The same map shows that Chicago is 560 miles in a direction 21.0 west of north from Atlanta. The figure below shows the location of these three cities. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago

Magnitude:
Direction:

One of the fastest recorded pitches in major-league baseball, thrown by Time Lincecum in 2009, was clocked at 101.0 mi/h. If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached home plate, 60.5 ft away?

A student stands at the edge of the cliff and throws a stone horizontally over the edge with a speed of 22.0 m/s. The cliff is h=54.0 m above a flat, horizontal beach
(a) What are the coordinates of the initial position of the stone?
(b) What are the components of the initial velocity?
(c) Write the equations for the x and y components of the velocity of the stone with time
(d) Write the equations for the position of the stone with time, using the coordinates in the figure
(e) How long after being released does the stone strike the beach below the cliff?
(f) With what speed and angle of impact does the stone land?

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 25 below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 3.97 m/s^2 for a distance of 35 m to the edge of the cliff, which is 30.0 m above the ocean.
(a) Find the cars position relative to the base of the cliff when the car lands in the ocean
(b) Find the length of time the car is in the air

A fireman d=40.0m away from a burning building directs a stream of water from a ground-level fire hose at an angle of 0=27 above the horizontal as shown in the figure. If the speed of the stream as it leaves the hose is v=40 m/s, at what height will the stream of water strike the building?

A car travels due east with a speed of 34 km/h. Raindrops are falling at a constant speed vertically with respect to the earth. The traces of the rain on the side windows of the car make an angle of 62 with the vertical. Find the velocity of the rain with respect to the following reference frames.
(a) The car
(b) The earth

A river has a steady speed of 0.680 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point.
(a) If the student can swim at a speed of 1.15 m/s in still water, how long does the trip take?
(b) How much time is required in still water for the same length swim?

An Alaskan rescue plane drops a package of emergency rations to stranded hikers. The plane is traveling horizontally at 40 m/s at a height of 100m above ground
(a) Where does the package strike the ground relative to the point at which it was released?
(b) What are the horizontal and vertical components of the velocity of the package just before it hits the ground?
(c) Find the angle of the impact

A long jumper leaves the ground at an angle of 20.0 to the horizontal and at a speed of 11.0 m/s.
(a) How long does it take for him to reach maximum height?
(b) What is the maximum height?
(c) How far does he jump?
(d) use equation 3.15c to find the maximum height he reaches

A ball is thrown upward from the top of a building at an angle of 30.0 to the horizontal and with an initial speed of 20.0 m/s. The point of release is 45.0 m above the ground.
(a) How long does it take fro the ball to hit the ground?
(b) Find the ball’s speed at impact
(c) Find the horizontal range of the stone. Neglect air resistance.

A train is traveling with a speed of 15 m/s relative to Earth. A passenger standing at the rear of the train pitches a baseball with a speed of 15 m/s relative to the end off the back end, in the direction opposite the motion of the train.
(a) what is the velocity of the baseball relative to the Earth?
(b) What is the velocity of the baseball relative to the Earth if thrown in the opposite direction at the same speed?

The boat in the figure is heading due north as it crosses a wide river with a velocity of 10.0 km/h relative to the water. The river has a uniform velocity of 5.00 km/h due east. Determine the magnitude and direction of the boat’s velocity with respect to an observer on the riverbank.

If the skipper of the boat in the same problem moves with the same speed of 10 km/h relative to the water but now wants to travel due north, in what direction should he head? What is the speed of the boat, according to an observer on the shore? The river is flowing east at 5.00 km/h