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What is a scalar?
A scalar is a quantity that has only magnitude but no direction.
What is a resultant vector?
A resultant vector is the vector sum of two or more vectors. It represents the combined effect of all the vectors.
What is a vector?
A vector is a quantity that has both magnitude and direction.
What is relative velocity?
Relative velocity is the velocity of an object as observed from a particular frame of reference.
Provide an example of a scalar quantity and a vector quantity.
Scalar quantity: Temperature
Vector quantity: Velocity
What is the shape of the path of a projectile?
The path of a projectile is a parabola.
What does it mean to resolve a vector?
To resolve a vector means to break it down into its components along the coordinate axes.
Describe an example of relative motion in everyday life.
A person walking on a moving walkway at an airport. The relative velocity of the person with respect to the ground is the sum of the person's walking speed and the speed of the walkway.
How can you add two vectors graphically?
Place the tail of the second vector at the head of the first vector. The resultant vector is drawn from the tail of the first vector to the head of the second vector.
What is the initial vertical velocity of a projectile launched horizontally?
Zero.
What is projectile motion?
Projectile motion is the motion of an object that is launched into the air, resulting in a curved, parabolic path.
How can you determine the relative velocity of one object with respect to another?
The relative velocity of object A with respect to object B can be found using the formula Vac = Vab + Vbc
How do you determine the net displacement when two displacement vectors are added?
By adding the two displacement vectors by breaking each vector into components and summing the components in each direction.
How do you use the tangent function to find the direction of a resultant vector?
Use the tangent function to find the angle θ of the resultant vector: tan(θ)=opp/adj.
How can the Pythagorean theorem be used in vector operations?
The Pythagorean theorem can be used to calculate the magnitude of a resultant vector when given its components.
What are the four properties of vectors?
1. Vectors can be moved parallel to themselves in a diagram.
2. Vectors can be added in any order.
3. To subtract a vector, add its opposite.
4. Multiplying or diving vectors by scalars, results in vectors.
Describe the horizontal and vertical components of a projectile’s motion.
The horizontal component of a projectile's motion is constant (assuming no air resistance), as there is no horizontal acceleration. The vertical component is affected by gravity, causing a constant downward acceleration.
Describe the method to determine the resultant vector when multiple vectors are involved.
Resolve each vector into its components. Sum all the x-components to get the resultant x-component, and sum all the y-components to get the resultant y-component. Combine these components using the Pythagorean theorem to find the magnitude and use the tangent function to find the direction of the resultant vector.
You are driving a car north at 50 km/h. Another car is driving south at 60 km/h. What is the velocity of the second car relative to you?
−110km/h
Explain how to add vectors that are not perpendicular to each other.
To add vectors that are not perpendicular, resolve each vector into its components, add the respective components along each axis, and then use the Pythagorean theorem and trigonometric functions to find the magnitude and direction of the resultant vector.