REGENTS PHYSICS – TWO DIMENSION KINEMACTIC OUTLINE
Two Dimensional Kinematics
1.2.0A-B Vectors
Vectors must be added by arranging them head-to-tail
A = 3 m at 20° B = 5 m at 160°
AX = 2.82 m
BX = -4.70 m
AY = 1.03 m
BY = 1.71 m
RX = -1.88 m
Ry = 2.74 m
1.2.0 Two Dimensional Motion - Constant Velocity in Both Dimensions
o When objects move in more than one dimension at a time (i.e. north-west), the motion can be broken
into two separate motions.
o
Trigonometry may be used to break the problem into two parts.
 Organize information into X/Y chart.

Use information to solve one dimension – time is the ONLY variable that can be used to cross
from one dimension to the other.

Pythagorean Theorem can also be used to find the resultant of two motions.
Example:
1. A hockey puck moves north with a speed of 6 meters per second. At the same time, the puck
drifts west at a speed of 2 meters per second. In the amount of time that it takes the puck to slide
24 meters north, it will also drift 8 meters west.
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REGENTS PHYSICS – TWO DIMENSION KINEMACTIC OUTLINE
2. The northward component of a boat’s velocity is 6 meters per second while the east ward
component of its velocity is 9 meters per second. The boat’s resultant velocity is 10.8 meters per
second. The boat will move with an angle that is 33.7° north of east.
1.2.1A-F Ground Launched Projectiles
o
Projectiles follow parabolic paths.
o
Break initial velocity into components (if not given).
o
Organize vertical and horizontal givens into a chart.
o
Make necessary assumptions
 ax = 0 (assume no air resistance)
 ay = -9.81 m/s2
 vix = vi cos θ
 viy = vi sin θ
 vy = 0 (at the maximum height)
 time to top = ½ total time of flight
o
o
o
For greatest height and/or flight time a projectile should be fired at 90°.
For greatest horizontal range a projectile should be fired at 45°.
Projectiles fired with the same speed at complementary angles will have the same horizontal range.
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REGENTS PHYSICS – TWO DIMENSION KINEMACTIC OUTLINE
Example:
1. A projectile is fired with an initial velocity of 12 meters per second at an angle of 30°. Breaking
the problem down we get…
1.2.1G-K Horizontally Launched Projectiles
Organize vertical and horizontal givens into a chart.
o Make necessary assumptions
 ax = 0 (assume no air resistance)
 ay = -9.81 m/s2
 viy = 0
 vix = initial velocity
 time is the same in both dimensions
o
Any two objects released from the same height will hit the ground at the same time regardless of
starting horizontal velocity!
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REGENTS PHYSICS – TWO DIMENSION KINEMACTIC OUTLINE
Example:
1. A projectile is fired horizontally with an initial velocity of 10 meters per second from a height of
6 meters above the ground. Breaking the problem down we get…
2. A projectile is fired horizontally from a height of 2 meters above the ground and travels 14 meters
horizontally before it lands.
3. A projectile is fired horizontally with a speed of 8 meters per second and travels 16 meters
horizontally before it lands.
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