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Projectile Motion in Two-Dimensions

A projectileis a body that moves near the earth's surface under the influence of the earth's gravityonly. Bullets and rocks are examples of projectiles whereas planes and rockets are not.

Objects than are thrown straight up into the air are projectiles. There are many other directions,however, in which a projectile can be propelled initially.

When a projectile moves in two dimensions, it is useful to look separately at its horizontal andvertical motions. It is common practice to represent the horizontal direction on the x-axis of acoordinate system and to represent the vertical on the y-axis. If air resistance can be ignored,projectiles move in parabolic paths.The projectile's horizontal and vertical motions are independent of each other.

We are going to watch a video showing a demonstration of projectile motion. Answer the questionsas we watch the video:

a. Describe the apparatus used to demonstrate projectile motion:

b. LISTEN carefully when Paul releases the spring. Do you hear the balls hit the ground at the same timeor are they different times?

c. What does Paul mean when he says, "Gravity doesn't take a holiday just because an object is moving."

Notice the Horizontal and the Vertical

motions are shown separately. Which of the

motions experiences no gravity? How can

you tell?

Which of the motions experiences gravity?

How can you tell?

http://www.exploratorium.edu/xref/phenomena/projectile_motion.htmlhttp://www.exploratorium.edu/xref/phenomena/projectile_motion.htmlhttp://www.exploratorium.edu/xref/phenomena/projectile_motion.html

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Lab Demonstration

In front of the class we have a canon that can shoot the ball with a velocity of 3.1m/s. Given that the initial velocity is

horizontal, our task is to set up a target so that the ball lands in it on the first try. Think we can do it?

1. Measure the vertical distance from the cannon to the top of the target. This distance should be measured to thenearest 100th of a meter.

2. Calculate the horizontal distance the object will travel (also to the nearest 100th of a meter).3. Measure out the correct distance and let it fly.

Equations:

Calculations:

Notes: Did it work? Did the ball reach the can?

Write Up

1. What is Projectile Motion? What are the main ideas of Projectile Motion?2. Describe the experiment. What was the problem we were trying to solve? What was given? What did we

measure?

3. Show your calculations for the Horizontal Distance.4. What is your conclusion? Does the theory work?

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Problems (on separate paper!):

1. A cannon ball leaves a fort with an initial horizontal speed of 180m/s and strikes a ship in thesea below 7.2 s later. What is the balls range? How high is the fort above sea level?

2. A plane flying with a steady horizontal speed drops a food package to a small isolated village.The package takes 7.5 s to fall to the village. If the package was released when the plane was ahorizontal distance of 3000 m from the village, determine:

i the plane's speed;ii the plane's altitude.

3. A man jumped horizontally from a window and reached the ground 0.80 s later. If he landed 3.6m from the base of the building, what was his initial speed? How high was the window above theground?

4. Santa Claus entered the North Pole Annual Elf Throwing Competition. He fired his elf with ahorizontal speed of 25 m/s from the top of an iceberg of height 110 m. What was the elfs rangeand time of flight?

5. A rocket was fired horizontally from a jet fighter plane. The rockets range was 5400m and itstime of flight was 21.0 s. Find the rockets initial speed and the altitude of the plane.

6. A steeplechase runner must jump from the top of a 2.0 m high fence and clear a water-filledditch below which is 3.0 m wide. If she jumps off the fence horizontally, at what speed must sheleave the fence?

7. A bullet was fired horizontally from the top of a 150-m tower at 280m/s. Find the bullets rangeand time of flight. Determine also its speed on impact with the ground below.