(Constant acceleration) Motion in a Plane (Constant acceleration)

(Constant acceleration) Motion in a Plane (Constant acceleration)

(Constant acceleration) Motion in a Plane (Constant acceleration) Example 1: A helicopter is in level flight with a constant horizontal speed of 11 m/s. At t = 0.0 s it begins to accelerate vertically at 0.96 m/s2. Assuming the helicopter’s acceleration remains constant for the time interval of interest, find… The horizontal and vertical distances through which it moves in 5.3 s, and Its x and y velocity components at t = 5.3 s.

The equations of motion for an object undergoing constant acceleration are: and What are the x- and y-components of the object’s initial position? A) x0 = 0 m, y0 = 0 m B) x0 = 1 m, y0 = 2 m C) x0 = 0 m, y0 = 2 m D) x0 = 1 m, y0 = 0 m E) x0 = 0 m, y0 = – 3 m

The equations of motion for an object undergoing constant acceleration are: and What are the x- and y-components of the object’s initial velocity? A) v0x = 0 m/s, v0y = 3 m/s B) v0x = 1 m/s, v0y = 2 m/s C) v0x = 0 m/s, v0y = 0 m/s D) v0x = 1 m/s, v0y = – 3m/s E) v0x = 0 m/s, v0y = – 3 m/s

The equations of motion for an object undergoing constant acceleration are: and What are the x- and y-components of the object’s acceleration? A) ax = 2 m/s2, ay = 0 m/s2 B) ax = 1 m/s2, ay = – 3 m/s2 C) ax = 0 m/s2, ay = – 6 m/s2 D) ax = 2 m/s2, ay = – 6m/s2 E) ax = 0 m/s2, ay = – 3 m/s2

Motion subject only to the force of gravity Projectile Motion Motion subject only to the force of gravity

Motion subject only to the force of gravity Projectile Motion Motion subject only to the force of gravity

Projectile Motion Properties Motion subject only to the force of gravity Properties Horizontal motion is independent of the vertical motion.

The red ball drops straight down The yellow ball has an initial horizontal motion Vertical motion is the same in each case

Horizontal motion is uniform for the yellow ball

Projectile Motion Properties Motion subject only to the force of gravity Properties Horizontal motion is independent of the vertical motion. x vs. t is linear, y vs. t is quadratic (parabolic) y vs. x is always parabolic

Projectile motion is always some part of a parabola Projectile motion displays symmetry between left and right sides

The angle between the initial velocity vector and the positive x-axis “Launch angle” The angle between the initial velocity vector and the positive x-axis General launch angle Zero launch angle

General Equations of Motion

General Equations of Motion Zero Launch Angle Equations of Motion (origin at the launch point)

Zero Launch Angle Example 2: A person skateboarding with constant speed 1.30 m/s releases a ball from a height of 1.25 m above the ground. Find… x and y for t = 0.250 s.

Zero Launch Angle Example 2: A person skateboarding with constant speed 1.30 m/s releases a ball from a height of 1.25 m above the ground. Find… x and y for t = 0.250 s. x and y for t = 0.500 s.

Zero Launch Angle Example 2: A person skateboarding with constant speed 1.30 m/s releases a ball from a height of 1.25 m above the ground. Find… x and y for t = 0.250 s. x and y for t = 0.500 s. the velocity, speed, and direction of motion of the ball at t = 0.500 s.