Objective questions about about chapter 3 ( Vectors )

The questions address the following topics 

اسئلة موضوعية على الفصل الثالث ( المتجهات ) ويدرس المواضيع التالية

 A swimmer heading directly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the current?

Solution

 1.2 m/s

A swimmer heading directly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still water?

Solution

 0.50 m/s

An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the origination of the flight. The plane flies with an air speed of 120 m/s. If a constant wind blows at 10.0 m/s due west during the flight, what direction must the plane fly relative to the air to arrive at the destination?

 4.78° east of north

A plane has an airspeed of 142 m/s. A 16.0 m/s wind is blowing southward at the same time as the plane is flying. If the velocity of the plane relative to Earth is due east, what is the magnitude of that velocity?

Solution

41 m 1/s

A plane has an airspeed of 142 m/s. A 30.0 m/s wind is blowing southward at the same time as the plane is flying. What must be the direction of the plane in order to move due east relative to the ground?

Solution

 12.2° north of east

A plane is headed eastward at a speed of 156 m/s. A 20.0 m/s wind is blowing southward at the same time as the plane is flying. The velocity of the plane relative to the ground is

 157 m/s at an angle 7.31° south of east

A car moves from a point located 26.0 m from the origin and at an angle of 35.0° from the x-axis to a point located 56.0 m from the origin and at an angle of 60.0° from the x-axis in 2.50 s. What is the magnitude of the average velocity of the car?

Solution

 13.7 m/s

A soccer player carries the ball for a distance of 40.0 m in the direction 42.0° west of south. Find the westward component of the ball's displacement.

 26.8 m

A player throws a football 74.0 m at 61.0° north of west. The westward component of the displacement of the football thrown is given by

 35.9 m.

A vector is located in the x-y plane. The x- and y-components of this vector are 4.00 m and 3.00 m, respectively. Find the angle that this vector makes with the positive y-axis.

Solution

 53.1°

A boat, whose speed in still water is 1.75 m/s, must aim upstream at an angle of 26.3° (with respect to a line perpendicular to the shore) in order to travel directly across the stream.

(a) Determine the speed of the current.

(b) Determine the resultant speed of the boat with respect to the shore.

Solution

(a) 0.775 m/s

(b) 1.57 m/s

You are trying to cross a river that flows due south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

Solution

 in a northwesterly direction.

If the acceleration of an object is always directed perpendicular to its velocity, then

Solution

the object is turning.

If the acceleration vector of an object is directed anti-parallel to the velocity vector, then

Solution

 the object is slowing down.

If the acceleration vector of an object is directed parallel to the velocity vector, then

 the object is speeding up.

A car travels along eastward with a constant velocity. The magnitude of the acceleration of the car is

Solution

 zero.

Under which of the following conditions would a car have a westward acceleration?

 A a car travels eastward with its velocity is decreasing.

A car travels along east and its velocity decreases. The acceleration of the car is in which of the following directions?

Solution

 Westward

Three vectors have equal magnitudes and make 120° with each other. We can say that

 the resultant is zero.

If three vectors add up to a zero resultant it is correct to say that

 the three vectors must be in a plane.

What is the smallest number of vectors that can be added to give a zero resultant?

Solution

 2

The sum of two vectors has the greatest magnitude when the angle between these two vectors is

Solution

 0°.

Which of the following statements is a true statement?

Solution

The magnitude of a vector cannot be zero unless all of its components are zero.

Which of the following is a vector quantity?

Solution

 displacement

Which of the following is a scalar quantity?

Solution

 mass

A car is moving with a constant speed along a circular track. The car is therefore not accelerating.

Solution

FALSE

If the velocity vector of a car in a particular direction is increasing, the acceleration vector of that car in the same direction must also be increasing.

Solution

FALSE

A scalar quantity multiplied by a unit vector is a scalar quantity.

FALSE

The magnitude of a unit vector is one

Solution

TRUE

A vector with zero magnitude can have one or more components that are nonzero.

Solution

FALSE

A component of a vector can be greater than the vector's magnitude.

Solution

FALSE

Vector quantities are represented in terms of their magnitude and direction.

Solution

TRUE

Mass is a vector quantity.

Solution

FALSE