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ACTIVITY THE MOTION OF PROJECTILES

INTRODUCTIONIn this activity you will begin to understand the nature of projectiles by mapping out the paths of two projectiles over time; the first moving horizontally

and the other projected at a 30° angle above the horizontal.

HORIZONTAL PROJECTILE (PROJECTED AT 15 M/S) 1. A rock is thrown horizontally from the top of a cliff. Calculate the horizontal position of the rock after each

second (using Equation 1) and place these positions in the table below. Assume the rock is moving horizontally at a constant speed of 15 m/s.

Show calculation for t = 3 s here: 2. Calculate the vertical positions of the rock for each second (using Equation 3) and place these positions in

the table below. Assume the rock is freefalling from rest. Show calculation for t = 3 s here:

Time (s) 0 1 2 3 4 5 6

Horizontal Position (m)

0 15

Vertical Position (m)

0 -4.9

3. Now plot ordered pairs of the horizontal and vertical positions of the rock in the graph below. Connect the

dots with a smooth curve in order to see the full path of the rock.

0 50 100

Horizontal Position (m)

0 -50 -100 -150

Vertical Position (m

)

Name (printed) _______________________________ First Day Stamp

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NON-HORIZONTAL PROJECTILE (PROJECTED AT 39 M/S AND AT AN ANGLE OF 30° ABOVE THE HORIZONTAL) 1. You must first determine the horizontal and vertical components of motion from the projection speed and

angle of the rock. Do this here: 2. Calculate the horizontal position of the rock after each second and place these positions in the table below.

Show calculation for t = 3 s here: 3. Calculate the vertical positions of the rock for each second and place these positions in the table below.

Show calculation for t = 3 s here:

Time (s) 0 1 2 3 4 5 6

Horizontal Position (m)

0 33.8

Vertical Position (m)

0 14.6

4. Now plot ordered pairs of the horizontal and vertical positions of the rock in the graph below. Connect the dots with a smooth curve in order to see the full path of the rock.

0 50 100 150 200

Horizontal Position (m)

20 0 -20 -40 -60

Vertical Position (m

)

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LABETTE HORIZONTAL PROJECTILE MOTION

INTRODUCTION What you’ve done earlier in this unit will enable you to understand projectile motion and this labette. As long as you understand constant speed and how objects accelerate under the influence of gravity, then you’re all set. As mentioned before, all projectiles are always in a state of doing two easy types of motion that are totally independent of each other – constant speed horizontally and freefall vertically. It means

that dealing with projectiles is no more difficult than other types of motion, just a bit longer, because you have to analyze both the vertical and the horizontal directions of motion separately. This labette will take you through a series of steps in which you deal with both directions of motion and hopefully illustrate their independence.

PRE-LAB PROBLEMS These must be checked with me before starting the labette.

1. A bully is pickin’ on you because he’s jealous of your physics ability. You know he’s a loser because he uses terms like “day glow” and pronounces nuclear “nuke-you-ler.” You tell him he’s out of his league and to prove it you claim to know projectile motion so well you can project an old rotten tomato horizontally so that it lands on his shoe, which is a horizontal distance of 15.0 m away. You throw the tomato horizontally at a speed of 23.8 m/s and it’s a direct hit! The bully takes off running; your honor is secure. What is the height of the tomato when it leaves your hand?

2. a. A very cool physics party is going on at the roof of a ten-story building when a physics boy begins to

choke on a chicken bone. A number of physics girls, who were trying to find a reason to hug the big guy anyway, pretend to give him the Heimlich Maneuver. It works, and the bone goes sailing out horizontally at 35 m above the ground. When the bone strikes the ground 21 m from the base of the building, the girls drop the big lug and dash for napkins in order to calculate the speed of the bone as it was projected from the guy’s mouth. Share their excitement and calculate the speed!

3. Two 10-year-old boys are doing dumb things that only 10-year-old boys do. One boy bets the other that he

can run horizontally across a rooftop and land safely on the roof of an adjacent building. The horizontal distance between the two buildings is 3.5 m, and the roof of the adjacent building is 2.4 m below the jumping off point. How fast does he have to run in order to make it?

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PURPOSE To use the equations of motion and the ideas of projectile motion to predict the range of a horizontal projectile.

PROCEDURE Fire the projectile launcher vertically into the air several times, measuring the maximum height of the metal ball

with a ruler each time.

DATA

Maximum Height of Ball (m)

Average maximum height of the ball: ________ Height above the ground the ball is launched: _______

QUESTIONS/CALCULATIONS (SHOW ALL WORK) 1. Use the maximum height of the ball to calculate its

initial speed.

Figure 10.5: Projectile Launcher

Trigger Cord – Pull away from launcher at a 90° angle.

Plumb Line – Used to measure angle of projection.

Horizontal and vertical position of projectile when launched.

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2. Now consider launching the ball horizontally from the launcher, with its horizontal speed being the speed calculated above. Set this up as a projectile motion problem and calculate what horizontal range the ball should have. You will also use the height the ball is launched from above the ground in this calculation. (Don’t actually shoot it until I come over to check your numbers and watch the shot with you.)

3. Measure the actual horizontal range and calculate the percent error. 4. Calculate the vertical velocity of the ball when it reaches the floor. 5. Now assume that when you were initially firing the launcher straight up that the ball had gone twice as far.

Also, assume that when you fire horizontally with this new speed, you do so from the top of your head. Calculate the new horizontal range and final vertical velocity of the ball. (Each partner does this for his or her own height. If you are the same height, have older partner add 5.0 cm to his/her height.)

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QUESTIONS AND PROBLEMS HORIZONTAL PROJECTILE MOTION

Do the following problems from the Giancoli book in the space provided below. Pages 66 – 71, Problems 26a, 35a, 64, 71a

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LABETTE PROJECTILE MOTION AT AN ANGLE

INTRODUCTION You’ve had some experience with projectiles now. What you learned and demonstrated was that projectile motion consists of two simultaneous and unrelated motions (constant speed horizontally and freefall vertically). However, the last labette only included objects that were projected horizontally. That’s really a trivial case though (it only includes projections at 0° and none of the other possible

angles). Yet, even when projectiles are fired at random angles, the same rules apply. The only difference is that you have to determine ahead of time what portion of the motion is initially vertical and what portion is initially horizontal. Although projectiles at an angle look far more complicated, there is absolutely no difference.

PURPOSE To use the equations of motion and the ideas of projectile motion to predict the

range of a steel ball projected at an angle above the horizontal.

PROCEDURE Fire the ball from the projectile launcher several times horizontally from the

top of a lab table, measuring its horizontal range each time. This can be used to determine the speed of the ball as it leaves the launcher.

DATA

Horizontal Range of the ball (m)

Average horizontal range of ball: ________ Height above the ground the ball is launched: ________

QUESTIONS/CALCULATIONS (SHOW ALL WORK) 1. Use the horizontal range of the ball and the height it is fired from to calculate the initial speed of the ball.

When you have calculated this speed, you will know the projectile speed when the launcher is at any angle.

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USE THE DIAGRAM BELOW TO MAKE CALCULATIONS 2 - 4.

2. Calculate the range of the ball if it is fired from the table at 30° above the horizontal, and lands on the floor.

The speed of the ball as it leaves the launcher (at the 30° angle) will be the speed you calculated in Question 1. (This range will be long enough that air resistance is usually a factor, so subtract 5 cm from your calculated range to compensate for this effect.)

3. Calculate the maximum altitude of the ball (from the floor). 4. Calculate the horizontal distance to where the ball’s maximum altitude is. 5. Measure the actual horizontal range of your ball, calculate the percent error. Carefully account for any

discrepancies.

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For each of the following questions, give clear and complete evidence for your choice in the space provided. 1. _____ One bullet is fired at an angle of 30° above the horizontal. A second bullet is fired at an angle of 30°

below the horizontal. After two seconds, both are still in the air. Which one has the greatest horizontal speed?

a. The first b. The second c. Both are the same 2. _____ One bullet is fired at an angle of 30° above the horizontal. A second bullet is fired at an angle of 30°

below the horizontal. After two seconds, both are still in the air. Which one has the greatest vertical speed?

a. The first b. The second c. Both are the same 3. _____ One bullet is fired at an angle of 30° above the horizontal. A second bullet is fired at an angle of 30°

below the horizontal. After two seconds, both are still in the air. Which one has the greatest acceleration? a. The first b. The second c. Both are the same 4. _____ One bullet is fired at an angle of 30° above the horizontal. A second bullet is fired at an angle of 30°

below the horizontal. After two seconds, both are still in the air. Which one has the greatest horizontal distance?

a. The first b. The second c. Both are the same 5. _____ A ball is kicked upward from the ground at a 40° angle and then moves as a projectile until it comes back

to the ground. Where is its least overall speed? a. Right after it is kicked d. Both “a” and “c” b. At its highest altitude e. “a,” “b,” and “c” c. Right before it reaches the ground again 6. _____ A ball is kicked upward from the ground at a 40° angle and then moves as a projectile until it comes back

to the ground. Where is its greatest overall speed? a. Right after it is kicked d. Both “a” and “c” b. At its highest altitude e. “a,” “b,” and “c” c. Right before it reaches the ground again

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QUESTIONS AND PROBLEMS PROJECTILE MOTION AT AN ANGLE

1. A bullet is fired from the ground with an initial speed of 1.70 x 102 m/s at an initial angle of 55.0° above

the horizontal. a. Neglecting air resistance and assuming the bullet lands at the same level it was fired from, find the

bullet’s horizontal range. b. How high does the bullet go? 2. A baseball player hits a baseball with an initial velocity of 55 m/s at an angle of 35° above the ground.

Where is the baseball (horizontally and vertically) 3.1 seconds after it is hit? 3. A thirteen-year-old boy wants to impress his friends by using his bicycle to jump over as many of these

friends as possible as they lie on the ground. He has them lie side by side next to a takeoff ramp. When he leaves the ramp he is 1.5 m above the ground, moving at 14 m/s and 18° above the horizontal. If each of his friends is 0.60 m wide, what is the maximum number of friends over which the cyclist can jump?

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4. Two high school wannabe baseball pitchers (Lora and Dora) challenge each other to a contest. They agree that they will each throw a baseball toward a tall building located 25 m away. The winner is the one who can hit the highest point on the building. Lora throws with a velocity of 25.0 m/s at an angle of 55.0° above the horizontal. Dora throws with a velocity of 28.0 m/s at an angle of 44° above the horizontal. Who wins, and by how much?

5. A golfer standing on a fairway hits a shot to a green that is elevated 5.0 m above the point where she is

standing. If the ball leaves her club with a velocity of 45 m/s at an angle of 42° above the ground, calculate how far away the green is.

6. A little leaguer hits his baseball into the air with an initial velocity of 35 m/s and 50.0° above the

horizontal. At the same time, the center fielder starts running away from the batter and catches the ball 1.85 m above the level at which it was hit. If the center fielder is initially 95.0 m from home plate, calculate his average speed.

7. You’re a baseball player, positioned 61 m from the batter. He hits the ball straight at you with an initial

speed of 25.0 m/s and 50° above the horizontal. When he hits the ball, it is 0.70 m above the ground. How high above the ground do you need to get your glove to catch the ball?

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Critical Thinking Questions 1.