Kinematics in two dimensions

1
Kinematics in two dimensions

• Position
• Displacement
• Average Velocity
• (Instantaneous) Velocity
• Average Acceleration
• (Instantaneous) Acceleration

2
Instantaneous velocity and acceleration
3
Constant acceleration
4
Projectile Motion
5
Mortars, artillery, and guns
Motion is parabolic!
6
2004 Report on the status of the Army Artillery
School

• ...And student officers with reading and math
  skills below seventh-grade level have been
  allowed to recycle multiple times before being
  force-fed to their units - even though an
  artillery officer who can't do math is like a
  fireman who's allergic to smoke.
• Columnist and former soldier David H. Hackworth
  is the author of The Price of Honor, and
  contributes weekly commentary to DefenseWatch

7
Example Problem

• A batter hits a pitched ball whose center is 4.0
  feet above the ground so that is angle of
  projection is 45 degrees and its range is 350
  feet. The ball will be a home run if it clears a
  24 ft high fence that is 320 feet from home
  plate. Will the ball clear the fence? If so, by
  how much?

8
Uniform Circular Motion

• Uniform magnitude of velocity (speed) is not
  changing

9
Uniform Circular Motion Terms

• Frequency (f) The number of revolutions
  (cycles) completed in a second.
• Period (T) The time to complete one revolution
  (cycle).

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Uniform Circular Motion Example

• A particle moves in a circular path 0.40 m in
  radius with constant speed. The particle makes
  5.0 revolutions in each second of its motion.
• Find the particles speed
• Find the particles acceleration

13 m/s
390 m/s2
11
Relative Motion
The velocity of an object relative to stationary
reference frame is equal to the velocity of an
object relative to a moving reference frame plus
the velocity of the moving reference frame.
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Relative Motion
There is a 3 knot westerly current. Your ship is
doing 10 knots by log. What course must you
steer to make course north good? What will be
your speed over ground?
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Mo Boards
0
1000 yds
3 min
090/15kts