2. HERE IS AN EXAMPLE OF ONE-DIMENSIONAL MOTION YOU’VE SEEN BEFORE
SO FAR IN THIS COURSE YOU HAVE BEEN STUDYING WHAT IS CALLED
ONE-DIMENSIONAL MOTION
ONE-DIMENSIONAL MOTION HAS A STRAIGHT LINE PATH – OBJECTS
MOVE BACK AND FORTH ALONG THIS ONE STRAIGHT LINE
HERE IS AN EXAMPLE OF ONE-DIMENSIONAL MOTION YOU’VE SEEN BEFORE

3. IMAGINE THE RED ARROW REPRESENTS THE MAN’S DISPLACEMENT
DRAWN ON A SET OF AXES
HIS MOTION IS PARALLEL TO ONLY ONE AXIS
THAT IS WHY IT IS ONE DIMENSIONAL MOTION

4. HERE’S ANOTHER EXAMPLE
AGAIN A SET OF AXES WITH A DISPLACEMENT
VECTOR ARROW IS DRAWN IN
THE MOTION OF THE BALL IS PARALLEL TO ONLY ONE AXIS (THE
VERTICAL AXIS THIS TIME) SO THE BALL’S MOTION IS ONE DIMENSIONAL

5. BUT SUPPOSE AN OBJECT’S MOTION IS PARALLEL TO MORE THAN
ONE AXIS, LIKE THIS GIRL’S MOTION
AGAIN AXES ARE DRAWN AND HER
DISPLACEMENT VECTOR IS DRAWN
FROM WHERE SHE STARTS TO WHERE
SHE STOPS, CONNECTING THE ENDS
OF HER CURVED PATH
SHE STARTS
HERE
PART OF HER MOTION IS PARALLEL
TO THE HORIZONTAL AXIS AND
ANOTHER PART IS PARALLEL TO THE
VERTICAL AXIS – THUS HER MOTION
IS PARALLEL TO TWO AXES
THIS IS TWO-DIMENSIONAL MOTION
SHE STOPS
HERE

6. THE FIRST EXAMPLE OF TWO-DIMENSIONAL MOTION WE WILL STUDY
WILL BE PROJECTILE MOTION
A PROJECTILE IS DEFINED AS:
ANY OBJECT THAT IS LAUNCHED INTO FREE FALL
NO MATTER WHAT THE OBJECT IS, IF IS LAUNCHED
THEN ALLOWED TO FREE FALL, THAT OBJECT
IS CALLED A PROJECTILE AND IS IN WHAT
PHYSICISTS CALL PROJECTILE MOTION

7. THE PROJECTILES WE WILL STUDY NOW WILL BE IN TWO-DIMENSIONAL MOTION
THE DIVER SHOWN AT THE RIGHT IS
MOVING HORIZONTALLY TO THE LEFT
AT THE SAME TIME HE IS MOVING
VERTICALLY DOWNWARD
THIS IS TWO-DIMENSIONAL MOTION
AND IT PRESENTS US WITH A
PROBLEM WE NEED TO RESOLVE

8. THEY CANNOT BE USED WHENEVER YOU PLEASE.
HERE ARE THE THREE KINEMATIC EQUATIONS WE HAVE USED
THESE EQUATIONS ARE RESTRICTED
THEY CANNOT BE USED WHENEVER YOU PLEASE.
WHAT ARE THE RESTRICTIONS ON THE KINEMATIC EQUATIONS?
THE ACCELERATION (a) MUST BE CONSTANT IN BOTH DIRECTION AND MAGNITUDE
2. THE OBJECT MUST BE IN ONE-DIMENSIONAL MOTION
THIS LAST RESTRICTION IS THE PROBLEM MENTIONED EARLIER:
THE KINEMATIC EQUATIONS ARE GOOD ONLY FOR ONE-DIMENSIONAL MOTION, BUT WE WANT TO STUDY TWO-DIMENSIONAL PROJECTILE MOTION
WHAT’S A PHYSICIST TO DO??

9. HERE’S HOW WE WILL RESOLVE THIS PROBLEM.
THE DIVER IS FALLING AND MOVING
TO THE LEFT SIMULTANEOUSLY.
TWO POINTS IN HIS MOTION
HAVE BEEN INDICATED BY RED
DOTS
WE WILL CALL THE TOP DOT THE
DIVER’S ORIGINAL POSITION, AND
THE BOTTOM DOT HIS FINAL POSITION
THE GREEN ARROW INDICATES HIS
DISPLACEMENT VECTOR ALONG THE
VERTICAL AXIS
THE ORANGE ARROW INDICATES HIS
DISPLACEMENT VECTOR ALONG THE
HORIZONTAL AXIS

10. HERE’S HOW WE WILL RESOLVE THIS PROBLEM.
THE GREEN LINE INDICATES HIS
DISPLACEMENT ALONG THE VERTICAL
AXIS
THE DIVER’S VERTICAL MOTION BY
ITSELF IS ONE DIMENSIONAL
SO WE CAN IGNORE HIS HORIZONTAL
MOTION, AND CONSIDER HIS VERTICAL
MOTION ALONE.
BECAUSE WE ARE CONSIDERING
ONLY THE VERTICAL ONE-DIMENSIONAL
MOTION, WE ARE ALLOWED TO
USE THE KINEMATIC EQUATIONS.

11. HERE’S HOW WE WILL RESOLVE THIS PROBLEM.
THE ORANGE ARROW INDICATES HIS
DISPLACEMENT VECTOR ALONG THE
HORIZONTAL AXIS
USING THE SAME LOGIC:
THE DIVER’S HORIZONTAL MOTION BY
ITSELF IS ONE DIMENSIONAL
SO WE CAN IGNORE HIS VERTICAL
MOTION, AND CONSIDER HIS
HORIZONTAL MOTION ALONE.
BECAUSE WE ARE CONSIDERING
ONLY THE HORIZONTAL ONE-
DIMENSIONAL MOTION, WE ARE
ALLOWED TO USE THE KINEMATIC
EQUATIONS.

12. HERE’S HOW WE WILL RESOLVE THIS PROBLEM.
PROBLEM SOLVED!
WE CAN USE THE KINEMATIC EQUATIONS
IF WE USE THEM ON THE HORIZONTAL
AND VERTICAL MOTIONS SEPARATELY
INSTEAD OF LOOKING AT PROJECTILE
MOTION AS ONE TWO-DIMENSIONAL
MOTION, WE WILL LOOK AT IT AS
TWO SEPARATE ONE-DIMENSIONAL
MOTIONS.

13. IN ORDER TO EXECUTE THIS SEPARATION OF MOTIONS ACCURATELY, YOU
WILL NEED TO FOLLOW A SERIES OF STEPS IN EVERY PROBLEM. THESE
STEPS ARE CALLED THE VECTOR COMMANDMENTS
VECTOR COMMANDMENTS
READ THE PROBLEM CAREFULLY, THEN DRAW A SKETCH OF THE SITUATION
DESCRIBED, INCLUDING THE SIGN CONVENTION YOU WILL USE. THE
DRAWING MUST INCLUDE ALL NECESSARY VECTORS AS ARROWS.
a) The sketch must show all given quantities.
b) The “necessary vectors” are those vectors that appear in the equations you will use
c) If the problem has a drawing in it, use that drawing instead of making your own, but
make sure all necessary vectors and given quantities are shown
2. WRITE OUT ALL NECESSARY VECTORS IN i-j NOTATION
a) All necessary vectors must be in i-j notation – even if you do not have all the
numerical values. Any quantity for which you do not have a value must be written
using the appropriate mathematical symbol
3. AFTER YOU HAVE COMPLETED STEPS 1 AND 2, YOU CAN BEGIN TO
SOLVE THE PROBLEM USING SELECTED KINEMATIC EQUATIONS

14. SINCE WE ARE GOING TO DEAL WITH THE VERTICAL AND HORIZONTAL
MOTIONS SEPARATELY, WE NEED TO INDICATE WHICH OF THE TWO WE
ARE WORKING WITH. WE WILL DO THE WITH THE SUBSCRIPTS (x) AND (y).
THESE ARE THE KINEMATIC EQUATIONS IN THEIR ORIGINAL FORM
HERE ARE THE KINEMATIC EQUATIONS FOR HORIZONTAL MOTION
WHY DOESN’T THE (t) HAVE AN (x) SUBSCRIPT?
HERE ARE THE KINEMATIC EQUATIONS FOR VERTICAL MOTION
ON A PIECE OF SCRATCH PAPER, WRITE OUT THE KINEMATIC EQUATIONS
FOR VERTICAL MOTION.

15. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
READ THE PROBLEM CAREFULLY, THEN DRAW A SKETCH OF THE SITUATION
DESCRIBED, INCLUDING THE SIGN CONVENTION YOU WILL USE.
WHEN MAKING THE SKETCH YOU INCLUDE ONLY THOSE DETAILS WHICH
ARE ESSENTIAL TO THE PROBLEM, AND YOU DO NOT ATTEMPT TO MAKE
A BEAUTIFUL ARTIST’S RENDERING OF THE SITUATION
THE SKETCH AT THE RIGHT SHOWS THE
SIGN CONVENTION, THE CLIFF AND
THE TIGER (REPRESENTED BY THE
RECTANGLE). THESE ARE THE ESSENTIALS.

16. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
READ THE PROBLEM CAREFULLY, THEN DRAW A SKETCH OF THE SITUATION
DESCRIBED, INCLUDING THE SIGN CONVENTION YOU WILL USE. THE
DRAWING MUST INCLUDE ALL NECESSARY VECTORS AS ARROWS.
a) The sketch must show all given quantities.
b) The “necessary vectors” are those vectors that appear in the equations you will use
HERE IS THE SKETCH WITH THE
NECESSARY VECTORS AND THE
GIVEN QUANTITIES INCLUDED.

17. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
2. WRITE OUT ALL NECESSARY VECTORS IN i-j NOTATION
a) All necessary vectors must be in i-j notation – even if you do not have all the
numerical values. Any quantity for which you do not have a value must be
written using the appropriate mathematical symbol
ONE OF THE NECESSARY VECTORS
WAS THE ACCELERATION VECTOR (a).
HOWEVER, WE CANNOT USE ANY OF
THE KINEMATIC EQUATIONS IF THE
ACCELERATION IN NOT CONSTANT.
WHAT DO WE KNOW ABOUT THE
ACCELERATION OF ANY PROJECTILE,
SUCH AS THE TIGRESS, WHICH IS BY
DEFINITION AN OBJECT IN FREE FALL?

18. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
2. WRITE OUT ALL NECESSARY VECTORS IN i-j NOTATION
a) All necessary vectors must be in i-j notation – even if you do not have all the
numerical values. Any quantity for which you do not have a value must be
written using the appropriate mathematical symbol
WRITE OUT THE i-j NOTATION FOR THE
TIGRESS’ ACCELERATION AS SHE FLIES
THROUGH THE AIR.
IS THIS WHAT YOU WROTE?

19. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
2. WRITE OUT ALL NECESSARY VECTORS IN i-j NOTATION
a) All necessary vectors must be in i-j notation – even if you do not have all the
numerical values. Any quantity for which you do not have a value must be
written using the appropriate mathematical symbol
BASED ON THE INFORMATION IN
THE PROBLEM AND THE SKETCH,
WRITE OUT THE (VO) IN i-j NOTATION
IS THIS WHAT YOU WROTE?

20. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
2. WRITE OUT ALL NECESSARY VECTORS IN i-j NOTATION
a) All necessary vectors must be in i-j notation – even if you do not have all the
numerical values. Any quantity for which you do not have a value must be
written using the appropriate mathematical symbol
THE LAST VECTOR WE NEED TO WRITE OUT IS THE DISPLACEMENT
VECTOR (S).
THE VERTICAL COMPONENT WAS GIVEN IN THE PROBLEM AND IS SHOWN IN THE SKETCH
HOWEVER, WE DO NOT KNOW A NUMERICAL VALUE FOR THE HORIZONTAL COMPONENT.
WRITE OUT THE i-j NOTATION
FOR THE (S) VECTOR

21. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
2. WRITE OUT ALL NECESSARY VECTORS IN i-j NOTATION
a) All necessary vectors must be in i-j notation – even if you do not have all the
numerical values. Any quantity for which you do not have a value must be
written using the appropriate mathematical symbol
YOU MIGHT THINK THIS IS CORRECT
BUT AS IT SAYS ABOVE “Any quantity for which you do not have a value must be written using the appropriate mathematical symbol”
WHAT IS THE CORRECT SYMBOL FOR THE HORIZONTAL COMPONENT OF THE DISPLACEMENT?

22. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
2. WRITE OUT ALL NECESSARY VECTORS IN i-j NOTATION
a) All necessary vectors must be in i-j notation – even if you do not have all the
numerical values. Any quantity for which you do not have a value must be
written using the appropriate mathematical symbol
THE SYMBOL FOR DISPLACEMENT IS (S)
THE SYMBOL FOR HORIZONTAL IS THE SUBSCRIPT (x).
THEREFORE, THE CORRECT SYMBOL FOR HORIZONTAL DISPLACEMENT IS ( SX )
AND THE i-j NOTATION FOR THE DISPLACEMENT VECTOR IS

23. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
THE SKETCH AND EQUATIONS AT THE RIGHT SHOW THE RESULTS OF THE FIRST TWO STEPS OF THE VECTOR COMMANDMENTS.
ALL OF THIS IS ONLY PREPARATION FOR FINDING THE ANSWER, WE HAVEN’T YET BEGUN TO WORK OUT THE SOLUTION, WHICH IS VECTOR COMMANDMENT STEP 3.

24. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
3. AFTER YOU HAVE COMPLETED STEPS 1 AND 2, YOU CAN BEGIN TO
SOLVE THE PROBLEM USING SELECTED KINEMATIC EQUATIONS
ANSWER THE FOLLOWING QUESTIONS ON SCRATCH PAPER
WHAT IS IT WE ARE ASKED TO FIND?
WRITE OUT THE KINEMATIC EQUATION FOR FINDING THE VALUE OF (Sx ).
WE ARE ASKED TO FIND THE TIGRESS’ HORIZONTAL DISPLACEMENT, THAT IS, THE (Sx )

25. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
3. AFTER YOU HAVE COMPLETED STEPS 1 AND 2, YOU CAN BEGIN TO
SOLVE THE PROBLEM USING SELECTED KINEMATIC EQUATIONS
ANSWER THE FOLLOWING QUESTIONS ON SCRATCH PAPER
IN ORDER TO FIND (SX ), FOR WHAT QUANTITIES DO WE NEED VALUES?
WE NEED (vox ), (ax ), and (t)
DO WE HAVE VALUES FOR ALL THESE QUANTITIES?
NO – WE DO NOT HAVE A VALUE FOR (t), THE TIME THE TIGRESS WAS FLYING THROUGH THE AIR.

26. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
3. AFTER YOU HAVE COMPLETED STEPS 1 AND 2, YOU CAN BEGIN TO
SOLVE THE PROBLEM USING SELECTED KINEMATIC EQUATIONS
IN ORDER TO USE THE EQUATION ABOVE, WE MUST FIRST GET A VALUE FOR THE TIME (t)
NOTE THAT THE TIME (t) THE TIGRESS TOOK TO FLY OUTWARD HORIZONTALLY WAS THE SAME AMOUNT OF TIME IT TOOK HER TO FREE FALL THE (3.8 M) FROM THE TOP OF THE CLIFF
IN OTHER WORDS, THE HORIZONTAL TIME (t) IS THE SAME AS THE VERTICAL TIME, ALSO (t).

27. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
3. AFTER YOU HAVE COMPLETED STEPS 1 AND 2, YOU CAN BEGIN TO
SOLVE THE PROBLEM USING SELECTED KINEMATIC EQUATIONS
WE CAN USE THE VERTICAL MOTION TO FIND OUT THE HORIZONTAL (AND VERTICAL) TIME(t)
ANSWER THE FOLLOWING QUESTION ON SCRATCH PAPER
WRITE OUT THE EQUATION FOR CALCULATING THE VERTICAL DISPLACEMENT
IS THIS WHAT YOU WROTE?

28. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
3. AFTER YOU HAVE COMPLETED STEPS 1 AND 2, YOU CAN BEGIN TO
SOLVE THE PROBLEM USING SELECTED KINEMATIC EQUATIONS
ANSWER THE FOLLOWING QUESTION ON SCRATCH PAPER
FROM THE EQUATION ABOVE AND THE VALUES GIVEN BELOW THE SKETCH AT THE RIGHT, WHAT IS THE TIME THE TIGRESS IS FLYING THROUGH THE AIR, BOTH VERTICALLY AND HORIZONTALLY?

29. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
3. AFTER YOU HAVE COMPLETED STEPS 1 AND 2, YOU CAN BEGIN TO
SOLVE THE PROBLEM USING SELECTED KINEMATIC EQUATIONS
NOTICE THAT WE GET TWO ANSWERS FOR THE TIME (t). HOWEVER, SINCE TIME CAN NEVER BE NEGATIVE WE THROW (-0.88) OUT BECAUSE IT IS PHYSICALLY IMPOSSIBLE.

30. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
3. AFTER YOU HAVE COMPLETED STEPS 1 AND 2, YOU CAN BEGIN TO
SOLVE THE PROBLEM USING SELECTED KINEMATIC EQUATIONS
ANSWER THE FOLLOWING QUESTION ON SCRATCH PAPER
NOW THAT WE KNOW THE TIGRESS WAS IN THE AIR FOR (0.88) SECONDS, GO AHEAD AND CALCULATE HOW FAR HORIZONTALLY SHE FLEW.

31. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
3. AFTER YOU HAVE COMPLETED STEPS 1 AND 2, YOU CAN BEGIN TO
SOLVE THE PROBLEM USING SELECTED KINEMATIC EQUATIONS
HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
THE TIGRESS LANDS TO THE RIGHT OF THE BASE OF THE CLIFF

32. EXAMPLE PROBLEM
A TIGRESS RUNS ALONG A LOW CLIFF, WHICH IS (3.8 m) HIGH, AT A SPEED
OF (24 m/s). SHE LEAPS HORIZONTALLY FROM THE CLIFF AND LANDS SAFELY
ON THE GROUND. HOW FAR FROM THE BASE OF THE CLIFF DOES SHE LAND?
THIS IS THE ENTIRE SOLUTION TO THE PROBLEM ABOVE

33. TWO IMPORTANT POINTS
1. YOU MUST FOLLOW THE VECTOR COMMANDMENTS, IN THE PROPER ORDER, LEAVING NOTHING OUT
2. SOLVING A PROJECTILE MOTION PROBLEM OFTEN REQUIRES THE USE OF MORE THAN ONE KINEMATIC EQUATION.