Projectile Motion Days 1 & 2 We will learn what projectile motion is and how to analyze it using equations I will apply my kinematics equations to two dimensions in projectile problems.

Warm ups 1. Find and pick up your hw quiz and exit ticket from the lab table. 2. Turn in any missing assignments to the bin. 3. Using what you know about kinematics and how the world works, try to complete the worksheet next to the bin to the best of your ability (we will re-do it together on the back later in the lesson) 4. Take your binder/notebook out for notes.

Projectile Motion This is motion that occurs in two dimensions: Horizontal motion is at constant velocity Vertical motion is accelerated by gravity

Projectile Motion The Law of Compound Motion When an object is moving in multiple directions, the motion in one dimension has no effect on motion in another dimension.

Projectile Motion Horizontal velocity is maintained by Horizontal velocity is maintained by inertia. Equal distance traveled during each second and Equal distance traveled during each second and constant velocity.

Projectile Motion Vertical velocity increases each second with the pull of gravity in free fall. Each second the ball goes 10 m/s faster than the previous second and a greater distance. 5 m 10 m/s 1 s 20 m 20 m/s 2 s 45 m 30 m/s 3 s 80 m 40 m/s 4 s

Projectile Motion The combined motion looks like this: The path is not a straight line but an arc of a parabola.

Worksheet from the warm up If 1.0 cm = 5.0 m, the cliff is 80 m high. It takes about 4 seconds to hit the ground. Assume g = 10 m/s 2 to make easier calculations How far as it fallen in… 1 second? 2 seconds? 3 seconds? 4 seconds?

Projectile Motion When projectiles are launched at an angle, the initial velocity has a horizontal and a vertical component. v vxvx vyvy

Projectile Motion The path of the cannon ball is in the shape of a parabola. The dimensions of the parabola are determined by the magnitude of thev x andv y components. The path of the cannon ball is in the shape of a parabola. The dimensions of the parabola are determined by the magnitude of the v x and v y components. vxvxvxvx vyvyvyvy

Projectile Motion If the angle of launch is high, velocityis much greater than velocity. The cannon ball goes higher in the air, but does not go as far. If the angle of launch is high, velocity v y is much greater than velocity v x. The cannon ball goes higher in the air, but does not go as far. vxvxvxvx vyvyvyvy

Projectile Motion If the angle of launch is low, velocityis much greater than velocity. The cannon ball goes farther, but does not go as high. If the angle of launch is low, velocity v x is much greater than velocity v y. The cannon ball goes farther, but does not go as high. visual vxvxvxvx vyvyvyvy

What equations do we use? Always analyze the x-direction and y-direction separately

Example problem The following figure shows an airplane moving horizontally with a constant velocity of 115 m/s at an altitude of 1050 meters. The plane releases a care package that falls to the ground along a curved trajectory. Ignoring air resistance, determine (1)The time required for the package to hit the ground (2)How far East the package travels during its fall

(1)Determine the time is takes for the care package to hit the ground (2)How far to the East has it travelled during its fall?

Example problem A soccer ball is kicked at 17.5 m/s at an angle of 30° above the horizontal 1. What are the vertical and horizontal components of the initial velocity? 2. How long (time) is the ball in the air? 3. What is the maximum height it reaches? 4. How far away does the ball land if no one intercepts it?

Example problem A soccer ball is kicked at 17.5 m/s at an angle of 20° above the horizontal 1. What are the vertical and horizontal components of the initial velocity? 2. How long is the ball in the air? 3. What is the maximum height it reaches? 4. How far away does the ball land if no one intercepts it?

Projectile Motion Web simulations. Links will be on my website. Archery Artillery

Homework Projectiles HW # 1 handout Homework quiz in 2 classes (next week) Announcement: SNHS will be available for tutoring during SLED starting this week