# AP Physics 1/Kinematics/Vectors and Scalars

Educational level: this is a secondary education resource.
In this lesson we will learn about vectors and scalars. Gaining a good understanding of these is crucial to physics and beyond. Below you will find a series of example problems, which you should always try to do first. Then you can read the solutions, followed by the contents. Finally, do the exercises at the end. :
* Example A
* Speed, such as "40 kph" or "3 m/s" is a scalar quantity. Velocity, such as "40 kph west" or " 3 m/s south" is a vector quantity. Compare these two values, then answer the question: What is a vector quantity? What is a scalar quantity?
* Example B
* Vector quantities are often represented by an arrow. These arrows are called vectors. The direction the arrow points represent the direction, and the length represents the magnitude. Consider the following:
* A plane is taxiing to the runway at 50 kilometers per hour due north. There is a crosswind with velocity 50 kilometers per hour east. What is the velocity of the plane?
* We know the answer to be about 70.71 kilometers due northeast. To get to this answer, we have to "add" the two vectors. Figure out how to do this.
* Example C
* A plane is flying at 900 kilometers per hour due north. There is s crosswind with velocity 50 kilometers per hour east. What is the velocity of the plane?
* Example A
* Speed, such as "40 kph" or "3 m/s" is a scalar quantity. Velocity, such as "40 kph west" or " 3 m/s south" is a vector quantity. Compare these two values, then answer the question: What is a vector quantity? What is a scalar quantity?
* Problems
* Do each of these problems on a separate piece of paper. Check your answers with the Solution Manual.
* 1. What is the resultant of the following vectors: 10 km/h north, 10 km/h east?
* 2. What is the resultant of the following vectors: 20 km/h west, 20 km/h south?
* 3. What is the resultant of the following vectors: 10 km/h heading 0, 20 km/h heading 90?
* 4. What is the resultant of the following vectors: 5 m/s heading 15, 10 m/s heading 180?
* 5. What is the resultant of the following vectors: 20 m/s heading 0, 5 m/s 250?
* 6. A force is acting on a pair of ropes as shown. Which rope has the greater tension?
* 7. A force is acting on a pair of ropes as shown. Which rope has the greater tension?
* 8. A force is acting on a pair of ropes as shown. Which rope has the greater tension?
* 9. A boat is in the ocean. It is being propelled by one motor at 25 kph north. A wind is acting on the boat at an angle of 60 degrees, shown below. The wind speed is 50 kph. What is the velocity of the boat?
* Challenge Problems
* These problems are especially challenging! Hints are listed in the hints manual and are randomly numbered.
* 10. The Equilibrium Rule states that if an object is in equilibrium, then the net force is zero. Use this to answer this problem: George is hanging on a pair of ropes as shown. One of the ropes is half the length of the other and they form a right angle. George's body is 300 N. Calculate the force on each of the ropes. Hints: 50, 101
* Go next
* Solution Manual: AP Physics 1/Solution Manual
* Hints Manual: AP Physics 1/Hints Manual
* Next Lesson: Lesson 2: Representing Motion Part 1
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