Q: If the quadcopter's position is given by $$x(t) = 4t$$ and $$y(t) = 2t$$, what is the direction of its velocity vector relative to the east (x-axis)?

$$\theta = \arctan\left(\frac{2}{4}\right) = \arctan(0.5) \approx 26.6^\circ$$\ north of east

Q: A quadcopter is at position $$(x, y) = (12, 5)$$ meters. What is the angle from the origin to the quadcopter relative to the x-axis?

$$\theta = \arctan\left(\frac{5}{12}\right) \approx 22.6^\circ$$

Question 1

A quadcopter is flying at a constant altitude above the ground. If its position at time $$t is $$given by $$x(t) = 5t$$ and $$y(t) = 3t^2$, what is the magnitude of its velocity at t = 2$ seconds?

Accepted Answer

$$\sqrt{5^2$ + (6)^2$} = \sqrt{61} \approx 7.81 m/s$$

Question 2

If the quadcopter's position is given by $$x(t) = 4t$$ and $$y(t) = 2t$$, what is the direction of its velocity vector relative to the east (x-axis)?

Accepted Answer

$$	heta = \arctan\left(\frac{2}{4}ight) = \arctan(0.5) \approx 26.6^\circ$$\ north of east

Question 3

A drone operator is at the origin. The quadcopter is at position $$(x, y) = (10, 10)$$ meters. What is the distance from the operator to the quadcopter?

Accepted Answer

$$\sqrt{10^2$ + 10^2$} = \sqrt{200} \approx 14.14 m$$

Question 4

If the quadcopter moves in the xy-plane such that its velocity vector is always perpendicular to its position vector relative to the origin, what type of path does it follow?

Accepted Answer

A circular path centered at the origin

Question 5

The quadcopter's position is given by $$x(t) = 6 \cos(\omega t)$$ and $$y(t) = 6 \sin(\omega t). $$What is the speed of the quadcopter?

Accepted Answer

$$v = 6\omega$$

Question 6

A quadcopter is flying such that its position is $$x(t) = 2t^2$ and y(t) = 3t$. What is the acceleration vector at t = 1$ s?

Accepted Answer

$$\vec{a} = (4, 0) m/s$^2$$

Question 7

If the quadcopter's velocity is $$\vec{v} = (v_x, v_y)$$ and it is moving northeast, which of the following must be true?

Accepted Answer

$$v_x \u003e 0$$ and $$v_y \u003e 0$$

Question 8

A quadcopter starts at the origin and moves with constant velocity $$\vec{v} = (3, 4) m/s. $$Where is it after 5 seconds?

Accepted Answer

$$(x, y) = (15, 20) m$$

Question 9

If the quadcopter's position is $$x(t) = 8t$$ and $$y(t) = 6t$$, what is the equation for its trajectory in the xy-plane?

Accepted Answer

$$y = \frac{6}{8}x = \frac{3}{4}x$$

Question 10

A quadcopter is flying at constant altitude and its position is given by $$x(t) = 10 \cos(t)$$, $$y(t) = 10 \sin(t). $$What is the radius of its path?

Accepted Answer

$$10 m$$

Question 11

If the quadcopter's velocity vector is $$\vec{v} = (v_x, v_y)$$ and its speed is $$v = 10 m/s$$, which of the following could be a possible velocity vector?

Accepted Answer

$$(6, 8) m/s$$

Question 12

A quadcopter moves such that $$x(t) = t^2$ and y(t) = 2t$. What is the instantaneous velocity vector at t = 3$ s?

Accepted Answer

$$\vec{v} = (6, 2) m/s$$

Question 13

If the quadcopter's position is $$x(t) = 5t$$ and $$y(t) = 5t$$, what is the angle of its velocity vector relative to the x-axis?

Accepted Answer

$$45^\circ$$

Question 14

A quadcopter is at position $$(x, y) = (12, 5)$$ meters. What is the angle from the origin to the quadcopter relative to the x-axis?

Accepted Answer

$$	heta = \arctan\left(\frac{5}{12}ight) \approx 22.6^\circ$$

Question 15

If the quadcopter's position is $$x(t) = 7t$$ and $$y(t) = 24t$$, what is its speed?

Accepted Answer

$$\sqrt{7^2$ + 24^2$} = 25 m/s$$

Question 16

A quadcopter is flying at constant altitude and its position is given by $$x(t) = 4t$$, $$y(t) = 3t. $$What is the equation for its distance from the origin at time $$t$$?

Accepted Answer

$$d = \sqrt{(4t)^2$ + (3t)^2$} = 5t$$

Question 17

If the quadcopter's position is $$x(t) = 2t$$ and $$y(t) = 2t$$, what is the equation for its trajectory?

Accepted Answer

$$y = x$$

Question 18

A quadcopter is flying at constant altitude and its position is given by $$x(t) = 5 \cos(2t)$$, $$y(t) = 5 \sin(2t). $$What is the angular speed of the quadcopter?

Accepted Answer

$$2$$ rad/s

Motion in Two Dimensions: Quadcopter Flight in the xy-Plane

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