PPTIntroduction to Projectiles

Developer Notes

  • Some of the more conceptual exercises could be moved to the sections on velocity and acceleration. It would be better to check at that time whether students get the difference between velocity and acceleration. At least the questions are preserved here for now.

Version / Date / Who / Revisions
05
06 / 2003/11/17 / dk /
  • Added version table
  • Put in standard section headings
  • Added Reading
  • added concept - objects fall at the same rate

07 / 2003/12/02 / dk /
  • added different masses to projectile demonstrator
  • re-arranged exercises and added more

08 / 2003/12/04 / dk /
  • added more conceptual questions

09 / 2004/06/24 / Sc /
  • changed teachers section from chart format to a prose format
  • eliminated directions for Proj. prediction and Car over cliff, as they are now separate activities

Goals

  • Students should understand that all objects on Earth fall at the same rate (less friction and air resistance).
  • Students should understand that motion at right angles is independent.
  • Students should be able to solve problems with constant velocity at right angles.
  • Students should be able to solve problems with constant velocity and constant acceleration at right angles.

Concepts & Skills Introduced

Area

/

Concept

physics / objects fall at the same rate (less friction and air resistance)
physics / motion at right angles is independent
physics / projectile motion

Time Required

Warm-up Question

Presentation

Here is a series of demonstrations to introduce projectiles.

To catch their interest and provide something to come back to in the last projectile activity, run an electric car off the edge of a table and let it crash (into a cushion). They’re the crime scene investigators – how fast was it going when it left the cliff? What data can they gather?

To review that freely falling objects accelerate at the same rate (9.8 m/s2 on Earth), drop two tennis balls. Which will land first? Roll two BBs down an incline. Which will hit the bottom first?

To show that freely falling objects accelerate at the same rate (even if it’s not straight down), and that motion at right angles is independent, use the Projectile Demonstrator. Do this as a POE.

  • Show the washer that drops straight down, then show the washer that is projected
  • Ask- “Which one will hit the floor first?” (P)
  • Show both at the same time (O)
  • Falling objects accelerate at the same rate, even if it’s not straight down. Motion at right angles is independent (~E)

Repeat the above POE with two objects of different masses, letting the more massive one go straight down. Repeat with less massive one straight down.

For discussion, set a ball on a board with the board level. The ball's acceleration due to gravity has no effect on its sideways motion. Roll the ball - same thing. Make the board vertical and there's no sideways motion. Tip the board and you get a mix.

To illustrate independence of motion with a less complex example, ask the following question and show the following demo.

  • Question- A boat is traveling 4 kph across a river. The river is 4 km wide. The river is flowing at 3 kph. How far downstream is the boat when it reaches the other side?
  • Demo- Run an electric car across a piece of plywood (a really slow car helps). First run the car with the plywood still. Then keep the car still while moving the plywood. Then pull the plywood in the direction 90o to the motion of the car.
  • How fast does it cross the plywood if the plywood is still vs. moving? Same.
  • How far downstream does it move with the plywood?

Vocabulary – projectile – an object moving under the influence of gravity (and air resistance, if there is any). We’re going to neglect air resistance in this section.

Assessment

Writing Prompts

Relevance

Answers to Exercises

Answers to Challenge/extension

Background

Problem

Materials

Procedure

Summary

Reading

What do a falling drop of rain and the moon have in common? They are projectiles. Their motion is affected only by gravity and air resistance. For the moon, there is very little air, so it is operating almost completely under the influence of gravity. A basketball shot toward the hoop, a bullet fired at a target, a satellite in orbit, and a car falling over a cliff are all projectiles. A rocket with its engines on is not a projectile because its engines affect its motion.

So far in our study of motion (kinematics), we have looked at objects traveling in straight lines, like a ball rolling down a ramp, or a falling tennis ball. A straight line has only one dimension, length. Projectiles travel primarily in two dimensions. One of the dimensions is down, motion influenced by gravity, like a dropped rock. The other dimension is sideways, like a thrown ball.

If two motions are at right angles, they will have no effect on each other. Place a ball on a level board, and gravity won't make it move. Roll the ball, and it won't speed up or slow down (except for friction). Remove the board and the ball will fall straight down, but won't go sideways. Tilt the board and the ball will accelerate at an angle down, combining the two motions.

An object could have two velocities, each constant. An example is a boat traveling across a current. If there were no cross current, the boat would go in a straight line. If the boat simply drifted with the current, it would go in a straight line, too. Put the two together and the boat will still go in a straight line, but at an angle. (The boat is not a projectile.)

You can find how much time the boat will take to cross the river if you know its speed straight across the river and the width of the river. Use t = d/v. You can find how far down stream it will go if you know the time it takes to cross and the speed of the current. Use d = vt. As long as the two velocities are at right angles to each other, they can be treated separately. For example, if a kayaker paddles straight across a 100 m wide river at 2 m/s, and the river is flowing at 1 m/s, the kayaker will take 50 s to cross the river.

t = 100 m / 2m/s = 50 s

The kayaker will not end up straight across the river, but will travel 50 m downstream because of the current.

d = 1 m/s  50 s = 50 m

For a projectile, the sideways velocity and the downward acceleration can be looked at separately, too, if they are at right angles to each other. If you throw a baseball straight sideways at 40 m/s, you know it will eventually hit the ground. But how far will it go before it does? You could use d = vt, but you need to know how long the ball will be in the air. How do you figure that? Everything on Earth has the same acceleration down, 9.8 m/s2 (ignore air resistance). All you have to know is how high the ball started from, then use t = (2d/a). If the ball leaves your hand 2 m above the ground, it will hit the ground in 0.64 s.

t = (22 m / 9.8 m/s2) = 0.64 s

So the ball will travel 25.6 m before it hits the ground.

d = 40 m/s  0.64 s = 25.6 m

Exercises

In all of these questions, neglect air resistance.

1)If there are 9 yellow M&Ms for every 13 red M&Ms, how many yellow M&Ms are there if you have 78 red ones?

2)Does a dropped object have a constant velocity or a constant acceleration?

3)Assuming there is no friction between a hockey puck and the ice, does a puck sliding across the ice have a constant velocity or a constant acceleration?

4)If you throw a ball straight sideways, in which direction does it have a constant velocity? In which direction is it accelerating?

5)Throw a ball straight up in the air.

a)What is its speed at the highest point?

b)What is its acceleration at the highest point?

6)If a ball is thrown horizontally at the same time that another ball is dropped from the same height, which will hit the ground first? Why?

7)If a paddler can paddle straight across a river in 1 hour when there is no current, will it take more, less, or the same amount of time when there is a current?

8)If a dropped ball takes 1 second to hit the ground, will a ball thrown straight sideways from the same height take more, less, or the same amount of time to hit the ground?

9)If ball A is dropped at the same time that ball B is thrown up at an angle, will A hit first, B hit first, or will they hit at the same time?

10)If ball A is dropped at the same time that ball B is thrown down at an angle, will A hit first, B hit first, or will they hit at the same time?

11)If ball A is thrown up at an angle, and ball B is dropped at the same instant A reaches its peak, and from the same height, will A hit first, B hit first, or will they hit at the same time?

12)If ball A is dropped from higher than ball B, and B is released at the instant A reaches B's height, will A hit first, B hit first, or will they hit at the same time?

13)If you dropped a rock off the top of a 125 m cliff, how long would it take to hit the bottom?

14)Two parts:

a)How long does it take for an object on Earth to fall 5 m?

b)The Earth is bigger than the moon, so gravity on Earth is greater than on the moon. The acceleration due to gravity on the moon is about 1/6 of Earth’s, or 1.6 m/s2. How long does it take for an object on the moon to fall 5 m?

15)You’re a bush pilot flying supplies to a hiker, and you can’t land your plane in the area, so you have to drop the supplies. If you drop the supply box out of the plane when you’re exactly above the target spot, where will it land? On the spot, before the spot, or after the spot? Why? Ignore air resistance.

16)Water is flowing along the Niagara River when it reaches the Falls and goes over. At what point(s) is the water traveling at a constant horizontal velocity? At what points is it traveling with a constant vertical acceleration?

17)If a bullet is fired at 1,000 m/s horizontally from a height of 1 m, how far will it go before it hits the ground?

18)If you throw a ball straight up in the air, and it takes 4 s total for it to go up and come down again, how high did it go?

19)What is the fastest speed a volleyball can cross the net horizontally and still land in the court? The net is 2.24 m high, and the distance from the net to the end line is 9 m.

20)Crime scene investigators find that a car first hit the ground 30 m from the point where it left the cliff. The cliff is 20 m high. What speed (in km/hr) was the car going when it left the cliff?

21)You’re the bush pilot again, dropping supplies to a hiker, but now you have instrumentation. You’ve lowered your speed as low as you can: 72 km/hr. Your altitude is also low at 45 m. How far (in meters) ahead of the drop location should you push the box of supplies out?

22)Use a grid for this problem, or draw a square grid.

a)Draw a picture of an object moving horizontally at 10 m/s. Make a mark for the object’s location each second. Each square is 5 m.

b)Draw a picture of an object falling, starting from the same point. Make a mark for the object’s location each second. Each square is 5 m.

c)Now join the two pictures together by marking the object’s combined location at each second.

d)What shape do you see?

e)Does this look like the path a falling object might take?

23)A kayaker paddles across the Mississippi river at a steady 1.5 kph. If there was no current, he’d go straight across, but the current is 0.8 kph. The river is 1.5 km wide.

a)How far downstream does he reach the other side?

b)Extension: What was his speed compared to the bottom of the river?

24)With no friction or air resistance, at what position or positions does the ball have the greatest velocity?

25)Same as question 1, except include friction and air resistance.

26)A battleship is moving along at a constant velocity. It fires a cannon shell straight up in the air at point B. The ship is at point D when the shell comes down. Where does the shell hit? Why?

27)If you throw a stone horizontally straight out from a cliff, and it hits the water 3 seconds later, do you have enough information to estimate how high the cliff is? If not, what other information do you need? If so, how high?

28)A punter in football kicks the ball so that stays in the air (has a hang time) of 4.4 s. Impress your friends and tell them about how high the ball went. (No, don't actually tell your friends in class. Write your answer.)

29)If a bullet is fired horizontally from a height of 1.5 m with a velocity of 900 m/s, how far will it go before it hits the ground?

30)An arrow is fired horizontally at the center of a target. If the target is 40 m away, how far below the center of the target will the arrow hit if it travels at 80 m/s? Ignore air resistance and the flight characteristics of an arrow.

Challenge/ extension

Glossary

projectile - an object moving under the influence of gravity and air resistance only

05.7 Intro to proj 09sc.docPage 1 of 10

dk