2. September 24-25, 2015

3. So far, we have studied free fall – the vertical (up/down) motion of an object that only experiences force due to gravity. What if I gave a freely falling object an initial horizontal velocity? Would the horizontal velocity affect the up / down motion of the object? Watch the Myth Busters compare the rate of falling of a dropped bullet versus a bullet fired from a gun Watch this And this Conclusions? Horizontal motion does NOT affect vertical motion. We will also see that vertical motion does NOT affect horizontal motion. This means we can solve projectile motion problems by dealing with horizontal and vertical motion separately.

4. Horizontally Launched Projectiles If a ball rolls along the table with constant horizontal velocity, then the moment it leaves the table, it has the same horizontal velocity with which it rolled along the table and zero vertical velocity. In the horizontal direction, there are no forces on the motion which means no acceleration. Horizontal velocity remains CONSTANT. The ball continues to travel horizontally through the air at exactly the same speed which it was rolling on the table.

5. Horizontally Launched Projectiles If a ball rolls along the table with constant horizontal velocity, then the moment it leaves the table, it has the same horizontal velocity with which it rolled along the table and zero vertical velocity. In vertical direction there is gravitational acceleration. The projectile accelerates downward at exactly the same rate as it would if it were just dropped. When these two motions are combined - vertical free fall motion and uniform horizontal motion - the trajectory will be a parabola. click me click me

6. Often, the projectiles are launched at an angle. To solve the problem, we resolve this initial velocity into its horizontal and vertical components. v vyvyvyvy  Horizontal component of motion for a projectile is completely independent of the vertical component of the motion. Their combined effects produce the variety of curved paths - parabolas that projectile follow. click me click me vxvxvxvx Vertical component v y is decreasing on the way up, becoming zero at the top, and increasing on the way down. Horizontal component v x is constant throughout the motion. Projectiles Launched at an Angle

7. Zookeeper who found the special way to feed monkey banana. If there was no gravity acting on either the banana or the monkey, banana moves in a straight line and the monkey does not fall once he lets go of the tree. As such, a banana aimed directly at the monkey will hit the monkey. The zookeeper aims above the monkey’s head.The banana misses the monkey, moving over his head. banana passes as far above the monkey's head as it was originally aimed. The zookeeper aims at the monkey and shoots the banana very fast. The banana reaches the monkey before the monkey has fallen very far. The zookeeper aims at the monkey and shoots the banana with a slow speed. Banana hits the monkey after the monkey has fallen considerably far.

8. In conclusion, the key to the zookeeper's dilemma is to aim directly at the monkey. Both banana and monkey experience the same acceleration since gravity causes all objects to accelerate at the same rate regardless of their mass. Since both banana and monkey experience the same acceleration each will fall equal amounts.

9. Check Your Understanding -- The Truck and The 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. Where will the ball land? 1)In front of the truck, 2) In the truck, 3) Behind the truck, 4) We need to know the velocity of th e truck and ball to answer How do you know?

10. IDEAL PATH ACTUAL PATH 75 0 30 0 15 0 60 0 45 0 R = 2 v i 2 sinθ cos θ the same range is obtained for two projection angles that add up to 90 0 Projectile thrown with the same speed at 30 0 and 60 0 will have the same range. The one at 30 0 remains in the air for a shorter time. What if we have air resistance? Air resistance shortens the range of the object, and the path is no longer a parabola. You won’t need to mathematically solve this, but you DO need to be able to describe how air resistance affects the motion. Range of Projectile Motion (when starting and ending height are equal) This is our only new equation!

11.  If a projectile launches and lands at the same height, what affects how far it travels? Initial speed and angle  What affects how long a projectile stays in the air? Height of launch relative to landing, and the vertical component of initial velocity. vertical component of initial velocity.

12.  How does a projectile’s vertical velocity change over time? It becomes more negative.  How does a projectile’s horizontal velocity change over time? It doesn’t change (if air resistance is ignored)  How does a projectile’s acceleration change over time? It doesn’t change (always 9.81 m/s 2 down)