Chapter five

1. Projectile Motion Chapter five

2. What is the difference between scalar and vector quantities? • What are some examples of vector quantities? • 75 mph east • 65 N downward • Scalar quantities with direction don’t make sense (10 kg north, 5 liters east, etc) Quick review

3. We already know how to calculate the resultant of two vectors going in either the same or opposite directions, either add or subtract OYB: An airplane traveling slowly north at 80km/h relative to the surrounding air encounters a tailwind of 20 km/h. What will be the resulting velocity? What would the resulting velocity be if it made a u-turn and flew into the wind? Velocity Vectors

4. Perpendicular vectors • The resultant of two perpendicular vectors is the diagonal of a rectangle constructed with the two vectors as sides. 3 5 4 Velocity vectors

5. Is there a special case for squares? Yes, the diagonal of a square is √2, times the length of one of its sides 1 √2 1 Velocity vectors

6. Suppose that an airplane normally flying at 80 km/h encounters wind at a right angle to its forward motion—a crosswind. Will the airplane fly faster or slower than 80 km/h? OYB

7. Surfing– If you want to increase your speed, what do you do? As you increase your angle relative to the wave front, the velocity also increases. Physics of sport

8. Two vectors at right angles that add up to a given vector are known as the components. Any vector can be “resolved” into two component vectors at right angles to each other. The process of determining the components of a vector is called a resolution. Components of vectors

9. A projectile is any object that moves through the air or space, acted on by only gravity (and air resistance, if any) • A stone thrown in the air, a cannonball shot from the cannon, a spacecraft circling Earth Projectile motion

10. The horizontal component of motion for a projectile is just like the horizontal motion of a ball rolling freely along a level surface without friction. • Without friction, a rolling ball moves at a constant velocity. • Ball would cover equal distances in equal intervals Projectile motion

11. The vertical component of a projectile’s velocity is like the motion for a freely falling object. • Gravity acts vertically downward • A projectile accelerates downward with increasing speed in the vertical direction covering a greater distance in each successive equal time interval • Or, if projected upward, the vertical distances of travel decrease with time on the way up Projectile motion

12. MOST IMPORTANT: horizontal component of motion for a projectile is independent of the vertical component of motion • They are completely independent, their combined effects produce the variety of curved paths the projectiles follow. • OYB: describe the components of projectile motion Projectile Motion

13. Which coin hit the ground first? Does your answer depend on the speed of the coin? Explain The downward motion of a horizontally launched projectile is the same as that of free fall. A projectile’s path is called its trajectory. Projectiles launched horizontally

14. Remember, vertical distance is independent of horizontal distance. With no gravity, a projectile would follow a straight-line path. But because of gravity, it falls beneath the line the same vertical distance it would fall if released from rest. What is the equation for distance in free fall? d=1/2(g)(t)2 Projectiles launched at an angle

15. If you toss a projectile skyward at some angle, it isn’t moving at the speed at which you threw the object. Why? The vertical distance a projectile falls below an imaginary straight-line path increases continually with time and is equal to 5t2 meters. Projectiles launched at an angle

16. How long does the force of the thrower act on a ball tossed into the air? A projectile is launched at an angle into the air. Neglecting air resistance, what is its vertical acceleration? What is its horizontal acceleration? oyb

17. Vertical range is affected by firing a projectile at a steeper or lesser angle. Which would give a higher vertical range and which a lower? • Horizontal range is also affected by the angle at which the projectile is launched. • Two different projection angles will have the same horizontal range, two that add up to 90 degrees. Projectiles launched at an angle

18. The maximum range horizontally is achieved at an angle of 45 degrees. • Where would this information come in handy? • Batting, make contact at a 45 degree angle • Throwing shot, discuss, or javelin Projectiles Launched at an angle

19. Acceleration due to gravity is the same coming up as going down, so speed it loses going up is the same speed it gains coming down. • Therefore, the projectile hits the ground with the same speed it originally had when it was projected upward from the ground. • OYB: Describe how far below an imaginary straight-line path a projectile falls Projectiles launched at an angle

20. Since the earth is curved, for long range projectiles we must account for the curvature. • If an object were projected fast enough, it will fall all the way around the Earth and become an Earth satellite. My own “cheese statement”