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Going over HW3.05

Announcement

• Quiz on Friday (Graphing and Projectile Motion)

• No HW due Wednesday

As the red ball rolls off the edge, a greenball is dropped from rest from the same

height at the same time

Which one will hit the ground first?

They will hitat the SAME

TIME!!!

Projectile Motion

Objective:1. To view projectile motion as a result of vector independence

The same time?!? How?!?

vix

The red ball has an initialHORIZONTAL velocity (vix)

But does not have any initialVERTICAL velocity (viy = 0)

The green ball falls from restand has no initialvelocity IN EITHER

DIRECTION!

viy and vix = 0

One Dimension at a Time

• Both balls begin with no VERTICAL VELOCITY

• Both fall the same VERTICAL DISTANCE

• Both fall with the same ACCELERATION

• This means that the time of flight IS THE SAME IN BOTH CASES

Sideways motion has no influence on time of flight (only height does)

MythBusters Video

• How does this actually look in real life?

Day 2 – Projectile Motion

Horizontally-Launched projectiles• In the x-direction, it has constant velocity• In the y-direction, it is in free fall (9.8m/s/s)

• The x and y components have absolutely no affect on each other! (This is called the independence of vectors)

• The time it takes for an object to fall completely depends on its height, not horizontal velocity.

Announcements

• Unit Exam on Kinematics next Thursday • No quiz on Friday • No homework due Friday

Regents Practice: Projectile Motion

The diagram below represents the path of an object after it was thrown.

What happens to the object’s acceleration as it travels from A to B?A. It decreases.B. It increases.C. It remains the same.D. It depends on how fast the object was thrown

A 0.2-kilogram red ball is thrown horizontally at a speed of 4 meters per second from a height of 3

meters. A 0.4-kilogram green ball is thrown horizontally from the same height at a speed of 8

meters per second. Compared to the time it takes the red ball to reach the ground, the time it takes the

green ball to reach the ground is

A. one-half as greatB. twice as greatC. the sameD. four times as great

An object was projected horizontally from a tall cliff. The diagram to the right represents the path of the object, neglecting friction.

1. How does the magnitude of the horizontal component of the object’s velocity at A compare with the magnitude of the horizontal component of the object’s velocity at point B? EXPLAIN.

2. How does the magnitude of thevertical component of the object’s velocity at point A compare with the magnitude of the vertical component of theobject’s velocity at point B? EXPLAIN.

An object was projected horizontally from a tall cliff. The diagram to the right represents the path of the object, neglecting friction.

1. How does the magnitude of the horizontal component of the object’s velocity at A compare with the magnitude of the horizontal component of the object’s velocity at point B? EXPLAIN.

2. How does the magnitude of thevertical component of the object’s velocity at point A compare with the magnitude of the vertical component of theobject’s velocity at point B? EXPLAIN.

The horizontal component remains unchanged (no acceleration)

The vertical component is increasing (vertically faster, a = 9.8 m/s/s)

independent

0

9.8m/s/s downward

Horizontal velocity

horizontal

horizontal

Day 2 – Angled Launch

Objective:To determine which launch angles result in maximum height, range, and time of flight

Activity: Experimenting with different Launch Angles

• Greatest Height?• Farthest Range?• Maximum time of flight?• How would all of this change if we had air

resistance? • Symmetry about 45º

https://phet.colorado.edu/en/simulation/projectile-motion

A projectile launched at an angle of 45�above the horizontal travels through the air. Compared to the projectile’s theoretical path with no air friction, the actual trajectory of the projectile with air friction isA. lower and shorterB. lower and longerC. higher and shorterD. higher and longer

A golf ball is hit at an angle of 45� above the horizontal. What is the acceleration of the golf

ball at the highest point in its trajectory? [Neglect friction.]

A. 9.8 m/s2 upwardB. 9.8 m/s2 downwardC. 6.9 m/s2 horizontalD. 0.0 m/s2

Try out HW3.06

I am not assigning it just yet. Tomorrow we learn how to do Quantitative projectile motion

problems and then you will work on 3.06 in class on Friday

Day 3 - Quantitative PM

Projectile Motion - Quantitative

Objective:To be able to solve PM problems involving actual quantities

Which forces are acting in the x and y directions? [Neglect air resistance]

Which forces are acting in the x and y directions? [Neglect air resistance]

•Y-direction: Net force = gravity -> gravitational acceleration (ay = 9.8m/s/s)

•X-direction: No net force -> no acceleration (ax = 0 m/s/s; neglect air resistance)

X and Y have no effect on each other!

The time it takes to fall depends on height,

not horizontal velocity

Note: This is also called the range.

Use displacement equation in each dimension

Assume a horizontal launch.

t = 1.75

∆x = 35m

1. A ball is thrown horizontally with a speed of 25 m/s off a ledge that is 20 meters high. a. What is the time of flight of the projectile?

b. How far away from the bottom of the ledge does the ball land?

1. A ball is thrown horizontally with a speed of 25 m/s off a ledge that is 20 meters high. a. What is the time of flight of the projectile?

2.02 s

b. How far away from the bottom of the ledge does the ball land? 50.5 m

2. A bomb is released from a plane flying level at an altitude of 20000 m. It lands 40000 m horizontally from where it was released. a. How long was the bomb in the air?

b. What was the plane's speed when the bomb was released?

2. A bomb is released from a plane flying level at an altitude of 20000 m. It lands 40000 m horizontally from where it was released. a. How long was the bomb in the air? 63.89 s

b. What was the plane's speed when the bomb was released? 626.1 m/s

3. A stone thrown horizontally at a speed of 25 m/s from the top of a cliff takes 14.2 seconds to reach the ground. a. How high is the cliff?

b. How far away does the stone hit the ground?

3. A stone thrown horizontally at a speed of 25 m/s from the top of a cliff takes 14.2 seconds to reach the ground. a. How high is the cliff? 988 m

b. How far away does the stone hit the ground? 355 m

4. A bridge is 150 m above a river. If a young boy spits horizontally at a speed of 6 m/s. a. How long will it take the spit to hit the

water below?

b. How far from the base of the bridge will it hit?

4. A bridge is 150 m above a river. If a young boy spits horizontally at a speed of 6 m/s. a. How long will it take the spit to hit the

water below? 5.53 s

b. How far from the base of the bridge will it hit? 33.2 m

5. A ball is thrown horizontally with a speed of 12 m/s and lands a distance of 36 m away. a. How long was the ball in the air?

b. How high was it thrown from?

5. A ball is thrown horizontally with a speed of 12 m/s and lands a distance of 36 m away. a. How long was the ball in the air? 3 s

b. How high was it thrown from? 44 m

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