4. 2D Kinematics

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?

A boy stands on a skateboard at rest and throws a ball horizontally to the right. Neglecting friction, which direction will the boy on the skateboard move as a result of the throw?

CALC A 100 g bead slides along a frictionless wire with the parabolic shape y = (2m^-1) x². Find an expression for a_y, the vertical component of acceleration, in terms of x, v_x, and a_x. Hint: Use the basic definitions of velocity and acceleration.

A race car moves along a circular track of radius $R$. If the car is located at a point on the track that is directly east of the center, how many radius lengths east of the track's center is the car's position?

A wheel rolls without slipping on a horizontal surface. At a given instant, which of the following best represents the velocity vector of point $P$ located at the top of the wheel relative to the ground?

A solid sphere of radius $R$ rolls without slipping along the x-axis. If its center moves from position $(x,y)$ = $(0,R)$ to $(4R,R)$, what is the magnitude of the displacement of the point on the sphere that was initially at the bottom (touching the ground)?

Which of the following diagrams correctly shows the direction of wind motion between a region of high atmospheric pressure ($P^{high}$) and a region of low atmospheric pressure ($P^{low}$) (neglecting the Coriolis effect)?

A particle leaves the origin with an initial velocity of $3m/s$ in the x-direction and $4m/s$ in the y-direction. What is the magnitude of its initial velocity?

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt², where α = 2.4 m/s and β = 1.2 m/s². (a) Sketch the path of the bird between t = 0 and t = 2.0 s.

(II) An airplane is traveling 815 km/h in a direction 41.5° west of north (Fig. 3–40). How far north and how far west has the plane traveled after 1.75 h? 

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt², where α = 2.4 m/s and β = 1.2 m/s². Calculate the velocity and acceleration vectors of the bird as functions of time.

A boat is traveling east across a river with a velocity of $5m/s$ relative to the water. The river flows north at $3m/s$. What is the magnitude of the boat's velocity relative to the ground?