Projectile MotionProjectiles (vertical, horizontal and at an angle)

Vertical KinematicsFreefall

KinematicsRemember our three kinematics:

a = (vf-vi)

t

∆ d = vit + (1/2)at2

vf2 = vi

2 + 2a∆d

FreefallFreefall refers to when an object is

falling in air with no air resistance.◦Obviously, there is air resistance in the

real world. We will not take that into account when performing our calculations. All of our problems will take place in a vacuum

Objects in freefall are constantly accelerated at a rate of -9.8 m/s2. This number is equal to the acceleration due to gravity.

Specific conditionsWhen an object is dropped:

◦ Initial velocity is equal to zero.◦Final velocity is the velocity before the object

hits whatever it will hit, so it is NOT zero.◦Final velocity, acceleration, and displacement

will always be negative because the object is traveling downward. Time is always positive. You may be complicated and set your coordinate

plane such that downward = positive and upward = negative. This will reverse the signs for final velocity, acceleration, and displacement. If you do this, WRITE OUT YOUR GIVENS AND SHOW YOUR WORK.

Diagramming the problem

PracticeThe observation deck of tall

skyscraper 370 m above the street. Determine the time required for a penny to free fall from the deck to the street below.

A stone is dropped into a deep well and is heard to hit the water 3.41 s after being dropped. Determine the depth of the well.

Specific conditions (cont.)When an object is thrown:

◦The problem must be split in HALF, the trip up and the trip down.

◦Conditions will be different dependent on which half you are solving for: The way down will be like normal freefall The way up will have a positive initial

velocity and displacement, and final velocity will be equal to zero. Acceleration is still negative, and never equal to zero.

Diagramming the problem

PracticeA kangaroo is capable of jumping to a

height of 2.62 m. Determine the takeoff speed of the kangaroo.

A baseball is popped straight up into the air and has a hang-time of 6.25 s. Determine the height to which the ball rises before it reaches its peak. (Hint: the time to rise to the peak is one-half the total hang-time.)

If Michael Jordan has a vertical leap of 1.29 m, then what is his takeoff speed and his hang time (total time to move upwards to the peak and then return to the ground)?

Assignment (Application of Content)Individually complete #45-46 on

p.74

Complete the worksheet about Free Fall Problems.

When all work is completed, we’ll head in the lab for a short vertical projectile lab.

Horizontal Projectilesx and y kinematicsChapter 6, section 1p.147-152

The basicsX-direction: vx = x/t

◦Velocity is constant, so ax = 0

y-direction: conditions for dropped free fall is true

Diagramming the problem

Practice problemAt practice, coach Creasy

decided to do tackling drills on a cliff. PJ was the unfortunate victim of his rage, and he was tackled horizontally off the cliff at 3.0 m/s and travels 9.0 m horizontally from the base of the cliff. Determine the height of the cliff.

One more practice problemThe coyote runs horizontally off

the cliff with a speed of 5 m/s and plunges 250 m to the ground below. What was the coyote’s final velocity (magnitude and direction)?

Book practicePractice p.150 #1-3

Angled Projectilesx, y, and angles (right triangles and vectors)

Projectiles at an angleX-direction is still the same!Y-direction changes from dropped

freefall to thrown free fall.

In this case, objects are thrown at an angle, not straight up like in the freefall problems.◦This means we’ll need…. VECTORS!

How to start a problemRead and write down all givens. Assign

them the correct variable. Write out all formulas.

Draw a picture. Include a beginning right triangle and an ending right triangle.

SOLVE FOR TIME!◦Remember that time connects the x and y

directions.Solve the problem, one unknown at a

time. Look back at your givens and formulas each time.

Here we go!

A friend and I, who happens to be exactly my height, were casually tossing a football. I threw it at an angle of 35o above the horizontal with a velocity of 1.24 m/s. Find the following:

a) Horizontal velocityb) Height that the football reachedc) Total time that the ball was in the aird) Final velocity (magnitude and direction)

Textbook practiceOpen to page 152 and complete

problems 4 and 5.

Combined Angled off a Cliff

A gazelle jumps off of a 35 m high cliff. The gazelle jumps with an initial velocity of 2.2 m/s at an angle of 53o with the horizontal. Find the follwing:a) Horizontal displacementb) Height above the cliff that the gazelle

reachedc) Total time that the gazelle was in the

aird) Final velocity (magnitude and direction)

Textbook practiceOpen to page 152 and complete

problem 6.vf = 32 m/s at 82o