Ch4 2D Motion

Vector A has a magnitude of 6.0 m and points 30° south of east. Vector B has a magnitude of 4.0 m and points 30° west of south. The resultant vector A + B is given by

7.2 m at an angle of 64° south of east.

Two forces are acting on an object as shown in the figure. Assume that all the quantities shown are accurate to three significant figures. (a) What is the magnitude of the resultant force on the object? (b) What is the direction of the resultant force?

a) 185 b) 77.8 degreee

Displacement vector A is 5.5 cm long and points along the +x-axis. Displacement vector B is 7.5 cm long and points at +30° to the -x-axis. (a) Determine the x and y components of vector A . (b) Determine the x and y components of vector B . (c) Determine the x and y components of the resultant of these two vectors. (d) Determine the magnitude and direction of the resultant of these two vectors.

a) Ax=5.5 cm Ay=0 cm b) Bx=-6.49519 cm By=3.75 cm c) x=-.995191 cm y=3.75 cm d) Magnitude: 3.87981 cm Direction: 104.863 degrees

A projectile is fired from ground level at an angle above the horizontal on an airless planet where g = 10.0 m/s2. The initial x and y components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long after firing does it take before the projectile hits the level ground?

10.0 seconds

A velocity vector has components 36 m/s westward and 22 m/s northward. What are the magnitude and direction of this vector?

148.57 degrees 42.19 m/s

A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?

18.1 m/s

Vector A has a magnitude of 6.0 m and points 30° east of south. Vector B has a magnitude of 4.0 m and points 30° west of north. The resultant vector A + B is given by

2.0 m at an angle of 30° east of south.

A football kicker is attempting a field goal from 44 m out. The ball is kicked and just clears the lower bar with a time of flight of 2.9 s. If the angle of the kick was 45°, what was the initial speed of the ball, assuming no air resistance?

21.5 m/s

A player throws a football 50.0 m at 61.0° north of west. What is the westward component of the displacement of the football?

24.2 m

A ball rolls over the edge of a platform with only a horizontal velocity. The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m. What is the horizontal velocity of the ball just before it touches the ground? Neglect air resistance.

35 m/s

Two vectors, of magnitudes 20 mm and 50 mm, are added together. Which one of the following is a possible value for the magnitude of the resultant?

40 mm

A person throws a ball horizontally from the top of a building that is 24.0 m above the ground level. The ball lands 100 m down range from the base of the building. What was the initial velocity of the ball? Neglect air resistance and use g = 9.81 m/s2.

45.2 m/s

Vector M = 4.00 m points eastward and vector N = 3.00 m points southward. The resultant vector M + N is given by

5.00 m at an angle of 36.9° south of east.

Three ropes are tied in a knot as shown in the figure. One student pulls on rope A with 1.0 pound of force, and another student pulls on rope B with 7.0 pounds of force. How hard and in what direction must you pull on rope C to balance the first two pulls? Give the direction by specifying the angle (clockwise or counterclockwise) of the pull with the direction of rope A.

6.55744 pounds of force at a 292.411 degrees counterclockwise angle

You walk 33 m to the north, then turn 60° to your right and walk another 45 m. How far are you from where you originally started?

68 m

Vector A has magnitude 2 units and is directed to the north. Vector B has magnitude 5 units and is directed to the south. Calculate the magnitude and direction of A - B .

7 units, north

A boy kicks a football with an initial velocity of 20 m/s at an angle of 25° above the horizontal. If we neglect air resistance, the magnitude of the acceleration of the ball while it is in flight is

9.8 m/s2.

The figure shows three vectors, A , B , and C , having magnitudes 7.0 cm, 6.0 cm, and 4.0 cm, respectively. Find the x and y components of the resultant of these three vectors.

Ax=6.06215 Ay=3.5 Bx=-5.19615 By=3 Cx=0 Cy=-4

Shown below are the velocity and acceleration vectors for an object in several different types of motion. In which case is the object slowing down and turning to its right?

E

If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude.

False

If three vectors add to zero, they must all have equal magnitudes.

False

Consider two vectors A and B shown in the figure. The difference A - B is best illustrated by

choice (c)

For general projectile motion with no air resistance, the horizontal component of a projectile's acceleration

is always zero.

A ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped vertically. Which object is traveling faster when it hits the level ground below if neither of them experiences any air resistance?

the ball

James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. If there is no air resistance, when they reach the lake below

the splashdown speed of John is larger than that of James.