Unit 2: 2-D Motion Review

Which vector model correctly describes a swimmer swimming 4 m/s East in an ocean current moving 2 m/s South?

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Tags

NGSS.MS-ESS2-6

A student is trying to find their displacement after walking 25 meters north, then turning around and walking 15 meters south. Which method is correct?

• The student should add the two legs of the trip together because displacement is the total distance traveled.

• The student should use the Pythagorean theorem to find the displacement because displacement is a vector, which means you have to draw a triangle.

• The student should subtract the two because they are in opposite directions, and the displacement is the vector from start to finish.

Answer explanation

The correct method is to subtract the distances because the student walks in opposite directions. Displacement is the straight-line distance from the starting point to the ending point, which is 25m north - 15m south = 10m north.

An airplane is flying at 55 m/s west in a wind, and the resultant velocity of the plane in the wind is 60 m/s west. What type of wind is blowing on the plane?

• Headwind (against)

• Tailwind (with)

• Crosswind (across)

Answer explanation

The airplane's speed is 55 m/s west, and the resultant velocity is 60 m/s west. This indicates that the wind is aiding the plane's motion, making it a tailwind (with).

Lilly is paddling her kayak at 3 m/s east in a river that has a current of 0.5 m/s west. What is her resultant velocity?

• 2.5 m/s east

• 3.5 m/s east

• 2.5 m/s west

• 3.5 m/s west

Answer explanation

Lilly's velocity east is 3 m/s, while the current west is 0.5 m/s. To find the resultant velocity, subtract the current from her speed: 3 m/s - 0.5 m/s = 2.5 m/s east. Thus, the correct answer is 2.5 m/s east.

Tags

NGSS.MS-PS2-2

Two students leave the 11th/12th grade office and walk to the cafeteria to get lunch. Student 1 takes the hallway past the library (solid line), and Student 2 takes the hallway past the art rooms (dashed line). How do the distances they traveled and their displacements compare?

• Student 1 and Student 2 traveled the same distance, but Student 1 had a smaller displacement.

• Student 1 and Student 2 had the same displacement, but Student 1 traveled a shorter distance.

• Student 1 and Student 2 had the same displacement and distance covered.

• Student 1 traveled a shorter distance and had a smaller displacement than Student 2.

Answer explanation

Both students end at the same cafeteria location, giving them the same displacement. However, Student 1's path is shorter than Student 2's, resulting in Student 1 traveling a shorter distance.

A teacher walks 12 meters north down the hallway and then 5 meters west across the classroom. What is the teacher's displacement?

• 17 meters NW

• 7 meters NW

• 15 meters 36.9° W of N

• 13 meters, 22.6° W of N

Answer explanation

The teacher's displacement can be calculated using the Pythagorean theorem: \(d = \sqrt{(12^2 + 5^2)} = 13\) meters. The angle is found using \(\tan^{-1}(5/12) \approx 22.6°\) W of N, making the correct answer 13 meters, 22.6° W of N.

A car drives 30 meters north, then 20 meters west, and finally 40 meters south to reach the gas pump at Bucee’s

What is the correct drawing of vectors?

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A cyclist travels 50 meters east, then 30 meters north, and finally 20 meters west to reach the park.

What is the correct displacement of the vectors?

• 30 m north; 70 m east

• 30 m north; 30 m east

• 50 m east; 20 m west

Answer explanation

The cyclist's total eastward movement is 50 m east minus 20 m west, resulting in 30 m east. The northward movement is 30 m. Thus, the correct displacement is 30 m north and 30 m east.

A ball is tossed horizontally into the air. When the ball begins to accelerate downward toward the earth, what can be said about the direction of the acceleration?

• It is pointing to the right (in the x direction)

• It is pointing downward (in the y direction)

• It points opposite its velocity.

• It points in the same direction as its velocity.

Answer explanation

The ball accelerates downward due to gravity, which acts in the y direction. Therefore, the correct answer is that the acceleration is pointing downward (in the y direction).

A stunt coordinator has been tasked with designing a stunt where a chase car drives off a cliff and lands on a gas station that is 100 m away from the cliff. He must make sure that the stunt car lands at exactly the correct spot so that the safety nets, cameras, and explosives all work. After some consideration, the stunt coordinator records the following measurements:

• Yes, he only needs the height of the cliff and the mass of the car.

• Yes, he only needs the height of the cliff and the speed of the car.

• Yes, he only needs the speed of the car and the mass of the car.

• He needs to collect more measurements.

Answer explanation

To ensure the stunt car lands accurately, the stunt coordinator needs the height of the cliff to calculate the time of flight and the speed of the car to determine the horizontal distance. Thus, he needs the height and speed.

Tags

NGSS.MS-PS2-4

NGSS.MS-PS2-2

NGSS.MS-ETS1-1

NGSS.MS-PS3-1