Precalc 6.1-6.3 review

Front

What is the directional angle in standard position for a vector pointing northwest?

Back

The directional angle in standard position for a vector pointing northwest is 315°.

Front

How do you calculate the resultant speed of an airplane given its airspeed and wind velocity?

Back

Use the formula: Resultant Speed = \sqrt{(V_{plane} \cos(\theta_{plane}) + V_{wind} \cos(\theta_{wind}))^2 + (V_{plane} \sin(\theta_{plane}) + V_{wind} \sin(\theta_{wind}))^2}.

Front

What is the formula for finding the combined force of two vectors given their magnitudes and angles?

Back

Use the formula: \( F_{combined} = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos(\theta)} \) where \( \theta \) is the angle between the two forces.

Front

Define orthogonal vectors.

Back

Orthogonal vectors are vectors that are perpendicular to each other, meaning their dot product is zero.

Front

What are parametric equations in the context of projectile motion?

Back

Parametric equations describe the motion of an object in terms of time, typically expressed as x(t) and y(t) for horizontal and vertical positions.

Front

How do you determine if two vectors are parallel?

Back

Two vectors are parallel if they have the same or opposite direction, which can be determined if one vector is a scalar multiple of the other.

Front

What is the significance of the angle in standard position?

Back

The angle in standard position is measured from the positive x-axis counterclockwise and is used to define the direction of a vector.

Front

How do you find the horizontal and vertical components of a vector?

Back

The horizontal component is found using \( V_x = V \cos(\theta) \) and the vertical component using \( V_y = V \sin(\theta) \).

Front

What is the formula for the vertical motion of a projectile under gravity?

Back

The vertical motion can be modeled by the equation: \( y(t) = -16t^2 + V_{y0}t + h_0 \), where \( V_{y0} \) is the initial vertical velocity and \( h_0 \) is the initial height.

Front

What is the relationship between the forces applied at angles and the resultant force?

Back

The resultant force can be found by breaking each force into its components and then summing those components.