Question 1

A particle moves east at constant velocity  for a time interval DT.It then moves north at a constant velocity, with the same speed as before, for another time interval DT.Finally it moves east again with the original velocity.At the instant an additional time interval DT has elapsed, which of the following are true about the average velocity and the average acceleration for the motion described?
A)The average velocity is  and the average acceleration is zero.
B)The average velocity is  and the average acceleration is not zero.
C)The average velocity is not  and the average acceleration is zero.
D)The average velocity is not  and the average acceleration is not zero.

Accepted Answer

The answer of A particle moves east at constant velocity...

Question 2

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 40 mph.How long will it take for the plane to travel 200 miles north?
A)one hour
B)more than one hour
C)less than one hour
D)more information is needed

Accepted Answer

The plane is moving directly towards its destination, which means it is not affected by the wind in the northward direction. However, the wind is blowing from west to east, so it will slow down the plane's progress towards the east. Therefore, the actual ground speed of the plane will be less than 200 mph. In fact, it will be the vector sum of the airspeed and the headwind component. Using vector addition, we can find that the ground speed of the plane is 193.65 mph (sqrt(200^2+40^2)=204.12 mph, but we subtract the 40 mph headwind component to get the ground speed). Therefore, it will take the plane more than one hour to travel 200 miles north (specifically, 1.03 hours or approximately 1 hour and 2 minutes).

Question 3

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?
A)52.5$\degree$N of E
B)52.5$\degree$ N or W
C)37.5$\degree$ N of W
D)36.9$\degree$ N of W

Accepted Answer

The answer of Plane A is flying at 400 mph...

Question 4

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

Accepted Answer

The answer of A plane is moving due north, directly...

Question 5

Four vectors all have the same magnitude.Vector 1 is at 30$\degree$, Vector 2 is at 135$\degree$, vector 3 is at 240$\degree$, and Vector 4 is at 315$\degree$.Which vector has the greatest magnitude x-component and which vector has the greatest magnitude y-component?
A)Vector 1, Vector 2
B)Vector 3, Vector 4
C)Vector 1, Vector 3
D)Vector 3, Vector 2

Accepted Answer

To find which vector has the greatest magnitude x-component, we need to look at the cosine of the angle between each vector and the x-axis. The cosine of each angle can be found using the formula: cos(angle) = x-component/magnitude.

For Vector 1, cos(30°) = √3/2, so the x-component is (magnitude)(cos 30°) = (magnitude)(√3/2)
For Vector 2, cos(135°) = -√2/2, so the x-component is (magnitude)(cos 135°) = (magnitude)(-√2/2)
For Vector 3, cos(240°) = -1/2, so the x-component is (magnitude)(cos 240°) = (magnitude)(-1/2)
For Vector 4, cos(315°) = √2/2, so the x-component is (magnitude)(cos 315°) = (magnitude)(√2/2)

Comparing all four, we see that Vector 1 has the greatest magnitude x-component.

To find which vector has the greatest magnitude y-component, we need to look at the sine of the angle between each vector and the y-axis. The sine of each angle can be found using the formula: sin(angle) = y-component/magnitude.

For Vector 1, sin(30°) = 1/2, so the y-component is (magnitude)(sin 30°) = (magnitude)(1/2)
For Vector 2, sin(135°) = -√2/2, so the y-component is (magnitude)(sin 135°) = (magnitude)(-√2/2)
For Vector 3, sin(240°) = -√3/2, so the y-component is (magnitude)(sin 240°) = (magnitude)(-√3/2)
For Vector 4, sin(315°) = -√2/2, so the y-component is (magnitude)(sin 315°) = (magnitude)(-√2/2)

Comparing all four, we see that Vector 3 has the greatest magnitude y-component.

Therefore, the answer is C: Vector 1 and Vector 3.

Question 6

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?
A)5.7$\degree$ W of N
B)10$\degree$ W of N
C)22$\degree$ W of N
D)11$\degree$E of N

Accepted Answer

The answer of A plane is moving due north, directly...

Question 7

Vector 1 is 7 units long and is at 70$\degree$Vector 2 is 5 units long and is at 225$\degree$.Vector 3 is 3 units long and is at 150$\degree$.Which vector has equal magnitude components?
A)Vector 1
B)Vector 2
C)Vector 3
D)None of the vectors has equal magnitude components.

Accepted Answer

The answer of Vector 1 is 7 units long and...

Question 8

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 speed of Plane B as observed from Plane A?
A)900 mph
B)640 mph
C)357 mph
D)100 mph

Accepted Answer

We can use vector addition to find the relative velocity of Plane B with respect to Plane A.

Let the velocity of Plane A be represented by vector A and the velocity of Plane B be represented by vector B. The angle between the two velocities is 45 degrees (northeast is halfway between north and east).

We can then use the Pythagorean theorem and trigonometry to find the magnitude and direction of the relative velocity vector C.

Magnitude of C = sqrt((400 mph)^2 + (500 mph)^2 - 2 * (400 mph) * (500 mph) * cos(45)) = 357 mph

Direction of C = arctan((400 mph) * sin(45) / (500 mph - (400 mph) * cos(45))) = 38.66 degrees east of north

Therefore, the speed of Plane B as observed from Plane A is 357 mph in the direction of 38.66 degrees east of north.

Question 9

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?
A)1 km/h
B)2 km/h
C)3 km/h
D)4 km/h

Accepted Answer

Let's say the speed of the boat relative to the water is "b" and the speed of the current is "c".

When the boat travels upstream, its effective speed is:

(b - c)

When the boat travels downstream, its effective speed is:

(b + c)

We know that in one hour, the boat traveled 10 km upstream and 14 km downstream.

Using the formula:

distance = speed x time

We can write two equations:

10 = (b - c) x 1

14 = (b + c) x 1

Solving for "b" and "c" simultaneously, we get:

b = 12 km/h

c = 2 km/h

Therefore, the speed of the current in the river is 2 km/h.

Question 10

Vectors  ,  , and  have magnitudes 6, 11, and 20.When these vectors are added, what is the least possible magnitude of their resultant?
A)25
B)15
C)2
D)3

Accepted Answer

The answer of Vectors  ,  , and ...

Question 11

A projectile is fired at an angle of elevation of 60$\degree$.Neglecting air resistance, what are possible angles in flight between the acceleration vector and the velocity vector?
A)160$\degree$and 40$\degree$
B)20$\degree$ and 70$\degree$
C)90$\degree$ and 60$\degree$
D)none of the above

Accepted Answer

When a projectile is fired at an angle of elevation, the acceleration vector (due to gravity) is always straight down towards the ground. The only variable is the direction of the velocity vector.

At the top of the projectile's trajectory, the velocity vector is perpendicular to the acceleration vector, so the angle between them is 90 degrees. As the projectile begins to fall back towards the ground, the angle between the velocity and acceleration vectors decreases.

Since the angle of elevation in this problem is 60 degrees, the initial velocity vector is also 60 degrees above the horizontal. Therefore, at the top of the trajectory, the velocity vector is pointing straight up and the angle between the velocity and acceleration vectors is 90 degrees.

As the projectile continues to fall, the angle between the velocity and acceleration vectors decreases. However, the only answer choice that includes 90 degrees as a possibility is C. Therefore, C is the best choice.

Quiz 3: Vectors and Two-Dimensional Motion

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 40 mph.How long will it take for the plane to travel 200 miles north?

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?

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?

Four vectors all have the same magnitude.Vector 1 is at 30 $\degree$ , Vector 2 is at 135 $\degree$ , vector 3 is at 240 $\degree$ , and Vector 4 is at 315 $\degree$ .Which vector has the greatest magnitude x-component and which vector has the greatest magnitude y-component?

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?

Vector 1 is 7 units long and is at 70 $\degree$ Vector 2 is 5 units long and is at 225 $\degree$ .Vector 3 is 3 units long and is at 150 $\degree$ .Which vector has equal magnitude components?

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 speed of Plane B as observed from Plane A?

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?

Vectors , , and have magnitudes 6, 11, and 20.When these vectors are added, what is the least possible magnitude of their resultant?

A projectile is fired at an angle of elevation of 60 $\degree$ .Neglecting air resistance, what are possible angles in flight between the acceleration vector and the velocity vector?