Projectile Motion

Chapter 3

Vector and Scalar Quantities• Vector Quantity – Requires both

magnitude and direction• Velocity and Acceleration = vector

quantities• Thrown Baseball• Scalar Quantity – Requires

magnitude only• Scalars can be added, subtracted,

multiplied and divided like normal numbers

Velocity Vectors

• An arrow is used to represent magnitude and direction of a vector quantity

• These arrows may be combined (as in combining two or more velocities)

• These are very useful when we get an object (airplane) moving a certain velocity and another (wind) moving at a different velocity

Velocity Vectors

• Should be drawn to scale• Must meet head to tow.• Draw examples• Cars, planes, arrows

Vector Addition

Vectors in other Directions

• When the vectors are not in the same direction, there are a few ways to figure out the resulting velocity.

• The easiest way is to box the two vectors and use the Pythagorean theorem

• For a perfect square, the hypotenuse is the square root of 2.

Vector Addition

• The hypotenuse, or line drawn between the two vectors, is called the resultant

• Any vector can be broken down into its parts

Vector Components

Try These• An airplane is moving North at a velocity

of 80 km/hr and there is a wind blowing West at 60 km/hr. What is the resulting velocity?

• A motor boat traveling 4 m/s, East encounters a current traveling 3.0 m/s, North. What is the resultant velocity of the motor boat? If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore? What distance downstream does the boat reach the opposite shore?

Try These

• A motor boat traveling 15 m/s, East encounters a current traveling 8.0 m/s, North. What is the resultant velocity of the motor boat? If the width of the river is 450 meters wide, then how much time does it take the boat to travel shore to shore? What distance downstream does the boat reach the opposite shore?

Now Try These

• In your book, page 40, 1-6, 19-26, and 29-34.

Projectile Motion• What is a projectile? – Throw ball• Projectiles near the surface of Earth

follow a curved path • This path is relatively simple when

viewed from its horizontal and vertical component separately

• The vertical component is like the free fall motion we already covered

• The horizontal component is completely independent of the vertical component (roll ball)

• These two independent variables combined make a curved path!

Projectile Motion

Projectile Motion

No Gravity With Gravity

Projectile Motion

Horizontally Launched Projectile(initial speed (vx) = 25 m//s)

• Time Horizontal Displacement (x)

• 0s 0m• 1s 25m• 2s 50m• 3s 75m• 4s 100m• 5s 125m

• Ts vxt

• Vertical Displacement (y)

• 0m• 25m• 50m• 75m• 100m• 125m• ½ gt2

Horizontally Launched Projectiles

• What will hit the ground first, a projectile launched horizontally, a projectile dropped straight down, or a project fired up?

The Plane and the Package

Upwardly Launched Projectiles• Toss a projectile into the air at some angle;

without gravity, the projectile would keep moving further away in a straight-line path

• Instead, the projectile is found directly below that point (d = 5t² to be exact) as if it had been dropped from there for that many seconds.

• Remember that there is no horizontal acceleration, so the projectile always moves equal horizontal distances in equal times

• The projectile always lands at the same angle that it was released at

Upwardly Launched Projectiles

• Draw cannonball, with parabolic arc and straight line (without gravity). The cannonball would move in a straight line with constant speed, and under every second would be the cannonball, a distance of 5t2

Upwardly Launched Projectiles

• Draw the cannonball with vectors, noticing that the horizontal component stays in the same direction.

• At the top, the vertical component approaches zero.

Upwardly Launched Projectiles

• We have been assuming that the angle of launch has been 45’

• What if the angle was other than that?• Assuming no air resistance, all would be

perfect parabolas with different heights and different distances traveled

• Angles fired at complements of 90’ will travel the same distance, but different heights

Upwardly Launched Projectiles

• This is all considered without air resistance, which results in a significantly shorter parabola.

• Without air resistance, 45’ makes for the farthest flying object.

Upwardly Launched Projectiles

Baseball

• A boy throws a baseball from a height of 5m. It travels 20 m. How fast did he throw the ball?

Truck and Ball

• Imagine a pickup truck moving with a constant speed along a city street. In the course of its motion, a ball is projected straight upwards by a launcher located in the bed of the truck. Imagine as well that the ball does not encounter a significant amount of air resistance. What will be the path of the ball and where will it be located with respect to the pickup truck?

Fast-Moving Projectiles—Satellites

• What if a ball were thrown so fast that the curvature of Earth came into play?

• If the ball was thrown fast enough to exactly match the curvature of Earth, it would go into orbit

• Satellite – a projectile moving fast enough to fall around Earth rather than into it (v = 8 km/s, or 18,000 mi/h)

• Due to air resistance, we launch our satellites into higher orbits so they will not burn up

Satellites

Launch Speed less than 8000 m/s Projectile falls to Earth

                                             

Launch Speed less than 8000 m/s Projectile falls to Earth

                                             

Launch Speed equal to 8000 m/s Projectile orbits Earth - Circular Path

                                             

Launch Speed greater than 8000 m/s Projectile orbits Earth - Elliptical Path

                                           

Now Try These

• In your book Page 40, numbers 8-18, 27-28, and 34-46.