4. 2D Kinematics

A frog's tongue moves at a constant speed of $2 m/s$. During a total time of $50 \mathrm{ms}$ (which is $\frac{1}{20}$ of a second), how far does the tongue reach?

A particle moves in the xy-plane such that its position as a function of time is given by $x=3t$ and $y=4\sin \left(\pi t\right)$, where $t$ is in seconds. A string is attached from the origin to the particle. At certain times, the string will be perfectly straight (i.e., the particle passes through the x-axis). Find the first time $t_1$ with $t_1>0$ when this is true.

A particle moves along a path such that its position in polar coordinates is given by $r=2\cos \left(t\right)$ ft and $\theta =\frac{t}{2}$ rad, where $t$ is in seconds. What is the displacement vector of the particle from $t=0$ to $t=2$ seconds?

In which situation is position best described using two dimensions?

Three particles are fixed on an $x$ axis at positions $x=2m$, $x=5m$, and $x=9m$. What is the displacement of a particle that moves from the first to the third position?

How can the position of a very tiny particle in two-dimensional motion be determined?

In the context of simulating or showing motion in an assembly, why must at least $1$ degree of freedom be maintained?

Which of the following best describes the direction of the vector field $f(x,y)$ where $f(x,y)=\frac{yi-xj}{x^2+y^2}$?

In a two-dimensional tug of war, two teams pull on a rope with forces represented by vectors $F_1$ and $F_2$. What does the net force on the rope equal?

A thin semicircular rod of radius $R$ lies in the $xy$-plane with its ends at $(R,0)$ and $(-R,0)$. What are the coordinates of the center of mass of the rod?

Which of the following types of motion requires acceleration in more than one plane ($\mathrm{multiplanar}\mathrm{acceleration}$)?

A helicopter in the drawing is moving horizontally at a constant velocity $v$. Which of the following best describes the path of a package dropped from the helicopter (neglecting air resistance)?

In a two-dimensional motion scenario, which of the following events occurred first if a particle moves from point $A$ to point $B$ and then to point $C$?

Rebecca is flying a drone at a constant height. If she moves the drone from point A at coordinates $(2,3)$ meters to point B at coordinates $(7,11)$ meters, what is the magnitude of the drone's displacement?

Which of the following does not accurately describe the concept of displacement in two-dimensional motion?