Cliff Problems and Projectile Motion Unit 3: 2D Motion Model Cliff Problems and Projectile Motion

What is a Projectile? A projectile is any object that once projected or dropped continues in motion by its own inertia (N1L) and is influenced only by the downward force of gravity. By definition, a projectile has a single force that acts upon it - the force of gravity. If there were any other force acting upon an object, then that object would not be a projectile

Cliff Problems

Projectile Animation

Three Variable Height of the Cliff (y) Distance the rock lands out (x) Velocity outward (vx) One of these will be missing in each type of problem. vx y x

Horizontally – no acceleration Add these formulas to your notes. Solving is as easy as finding time first from the horizontal or vertical, then sub in to the other Horizontally – no acceleration Vertically – acceleration due to gravity (10m/s/s) x = vx * t ½ g

If you know the height of the cliff, use it to calculate time the projectile will be in the air. Remember, it is the same time it would have if it fell STRAIGHT DOWN. y = ½ g t 2 125 = ½ (10) t 2 t = 5 seconds During this time, the projectile travels straight out from the cliff with an unchanging speed of 15 m/s. It does this for 5 seconds. x = vxt x = (15)(5) = 75 meters

If you know the height of the cliff, use it to calculate time the projectile will be in the air. Remember, it is the same time it would have if it fell STRAIGHT DOWN. y = ½ g t 2 80 = ½ (10) t 2 t = 4 seconds During this time, the projectile travels straight out from the cliff with an unchanging speed and lands 24 m away. It does this in 4 seconds. x = vxt 24 = (v)(4) V= 6 m/s

If you don’t know the height of the cliff, use the horizontal speed and distance to find the time. x = vxt 45 = (15) t t = 3 seconds Now that you know the time, you know how far the projectile will fall. It is the same as the distance an object would fall if it fell straight down. y = ½ g t2 y = ½ (10) 32 y = 45 meters (this is the height of the cliff)

Horizontally Launched Projectile Animation Non-horizontally Launched Projectile Animation

Projectiles Footballs and Arrows

Remember the cliff problems?

Projectile Motion

The forward speed remains constant. The vertical speed decreases to zero then increases on the way down.

Up and down are mirror images of each other.

Projectile Motion Pairs of angles share the same range.

What is the range of this projectile?

Find components of the velocity – the vertical and horizontal parts.

Drawing – Measure to a scale and convert.

Or.. Use trig.

Which component determines how long the projectile will stay in the air? The vertical!

Remember: vy = a*t the time for a projectile to rise to its peak is a matter of dividing the vertical component of the initial velocity (viy) by the acceleration of gravity Multiply by 2 to get the total time of the flight up and down.

x = vxt Total time of flight Horizontal component of velocity How far away will the projectile go? This is not simply the horizontal component; but the horizontal component x 2

How much time? Up and down? Or only up? y Time up only!