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Exam 3: Vectors and Two-Dimensional Motion

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Question 1

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A plane is moving due north,directly towards its destination.Its airspeed is 200 mph.A constant breeze is blowing from west to east at 30 mph.At what rate is the plane moving north?

A) 198 mph
B) 193 mph
C) 188 mph
D) 180 mph

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Question 2

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In a 2-dimensional Cartesian coordinate system the x-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and x-axis?

A) sine
B) cosine
C) tangent
D) cotangent

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Question 3

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A bridge that was 5.0 m long has been washed out by the rain several days ago.How fast must a car be going to successfully jump the stream? Although the road is level on both sides of the bridge,the road on the far side is 2.0 m lower than the road on this side.

The first displacement is 6 m,and the second displacement is 3 m.They cannot add together to give a total displacement of:

A boat travels upstream and after one hour has gone 10 km.The boat next travels downstream and after one hour has gone 14 km.If the boat's speed relative to the water is constant,what is the speed of the current in the river?

Plane A is flying at 400 mph in the northeast direction relative to the earth.Plane B is flying at 500 mph in the north direction relative to the earth.What is the direction of motion of Plane B as observed from Plane A?

Five boys are pushing on a snowball,and each is pushing with a force of 10.0 N.However,each boy is pushing in a different direction.They are pushing north,northeast,east,southeast,and south.(Each boy is pushing at an angle of 45.0 $\degree$ relative to his neighbor. ) What is the magnitude of the total force on the ball?

A string attached to an airborne kite is maintained at an angle of 40 $\degree$ with the horizontal.If a total of 120 m of string is reeled in while bringing the kite back to the ground,what is the horizontal displacement of the kite in the process? (Assume the kite string doesn't sag. )

Which type of quantity is characterized by both magnitude and direction?

A stone is thrown at an angle of 30 $\degree$ above the horizontal from the top edge of a cliff with an initial speed of 12 m/s.A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.6 s.How far out from the cliff's edge does the stone travel horizontally? (g = 9.8 m/s² and air resistance is negligible)

A car is initially moving at 20 m/s east,and a little while later it is moving at 10 m/s north.Which of the following best describes the orientation of the average acceleration during this time interval?

Arvin the Ant travels 30 cm eastward,then 25 cm northward,and finally 15 cm westward.What is Arvin's direction of displacement with respect to his original position?

A fireman,50.0 m away from a burning building,directs a stream of water from a fire hose at an angle of 30.0 $\degree$ above the horizontal.If the initial speed of the stream is 40.0 m/s,at what height will the stream of water strike the building?

A stone is thrown with an initial speed of 15 m/s at an angle of 53 $\degree$ above the horizontal from the top of a 35 m building.If g = 9.8 m/s² and air resistance is negligible,then what is the magnitude of the vertical velocity component of the rock as it hits the ground?

When we subtract a velocity vector from another velocity vector,the result is:

A plane is moving due north,directly towards its destination.Its airspeed is 200 mph.A constant breeze is blowing from west to east at 20 mph.In which direction is the plane pointed?

In a 2-dimensional Cartesian coordinate system the y-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function,with respect to the angle between vector and y-axis?

A student adds two vectors with magnitudes of 200 and 40.Which one of the following is the only possible choice for the magnitude of the resultant?

Find the resultant of the following two vectors: i) 50 units due east and ii) 100 units 30 $\degree$ north of west.

I walk six miles in a straight line in a direction north of east,and I end up two miles east and several miles north.How many degrees north of east have I walked?