Projectile Motion Projectiles vertical horizontal and at an

Projectile Motion Projectiles (vertical, horizontal and at an angle)

Vertical Kinematics Freefall

Kinematics �Remember our three kinematics: �a = (vf-vi) t �∆ d = vit + (1/2)at 2 �vf 2 = vi 2 + 2 a∆d

Freefall �Freefall 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/s 2. This number is equal to the acceleration due to gravity.

Specific conditions �When 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

Practice �The 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

Practice �A 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 Projectiles x and y kinematics Chapter 6, section 1 p. 147 -152

The basics �X-direction: vx = x/t ◦ Velocity is constant, so ax = 0 � y-direction: conditions for dropped free fall is true

Diagramming the problem

Practice problem �At 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 problem �The 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 practice �Practice p. 150 #1 -3

Angled Projectiles x, y, and angles (right triangles and vectors)

Projectiles at an angle �X-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 problem �Read 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 35 o above the horizontal with a velocity of 1. 24 m/s. Find the following: a) b) c) d) Horizontal velocity Height that the football reached Total time that the ball was in the air Final velocity (magnitude and direction)

Textbook practice �Open 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 53 o with the horizontal. Find the follwing: a) Horizontal displacement b) Height above the cliff that the gazelle reached c) Total time that the gazelle was in the air d) Final velocity (magnitude and direction)

Textbook practice �Open to page 152 and complete problem 6. vf = 32 m/s at 82 o