1 chapter 6: motion in a plane. 2 position and velocity in 2-d displacement velocity average...
TRANSCRIPT
2
Position and Velocity in 2-D
Displacement Velocity Average velocity Instantaneous
velocity Instantaneous
acceleration Average acceleration
3
Directions of Instantaneous and average velocities
Instantaneous velocity at any point on the curve is along the tangent drawn at that point
Average velocity points in the direction of the displacement vector
7
If a particle’s motion is governed by x=2t2 and y=5t
At any time• What would be its displacement, velocity, and
acceleration?
• What would be its speed?
• What is the angle of inclination?
At t = 5 s• What would be its position, velocity, and acceleration?
• Calculate its speed
• Calculate its angle of inclination θ
8
Projectile Motion
A projectile is an object that moves in 2-D under the influence of only the gravitational force
For projectiles, ax=0 and ay=-g
9
Components of velocity and acceleration of a Projectile A projectile is launched
with an initial velocity (9.8,19.6) m/s
Observe that the x-component of velocity is not changing (no change in the length or direction)
Vertical component of the velocity is changing in length and direction due to gravitational force!
10
Dynamics of a projectile
Projectile motion is made up of two independent motionsUniform motion with constant velocity along x- direction (horizontal)Free-fall motion in the vertical direction
11
Range of a Projectile
Range is the longest horizontal distance traveled by a projectile
What should be θ for the projectile to have longest range?
When would the projectile reach maximum height?