1. Aim: How do we describe projectile motion when projectiles are launched At an Angle?

2. A projectile launched at an angle
This is what the path of a projectile looks like when it is launched at an angle.
Range = the horizontal distance that the projectile travels

3. Analyzing Projectile Motion
What happens to the vertical velocity of the projectile as it rises and falls? It decreases and then increases
What happens to the horizontal velocity of the projectile as it rises and falls? It stays constant
At what point is the projectile’s vertical velocity always zero? At the peak
Compare the time it takes projectile to rise with the time it takes projectile to fall (the same distance) It takes the same amount of time to rise and fall

4. Analyzing Projectile Motion

5. Analyzing Projectile Motion
Describe the velocity vector’s position with respect to the projectile’s trajectory.

6. Problem 1
A long jumper leaves the ground with an initial velocity of 12 m/s at an angle of 28-degrees above the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the long-jumper.

8. Projectile-Launched from a cliff

9. General Problem Solving Strategies
Find the components of initial velocity.
Write known and unknown quantities in both vertical and horizontal directions.
Select appropriate direction and apply Newton’s equations of motion.
Note the following: Acceleration is -9.8 m/s2 in the vertical direction, vertical velocity is 0 at peak height, and horizontal velocity does not change.

10. Problem 2
A stone is thrown at an angle of 30 degrees to the horizontal and with an initial speed of 20.0 m/s. a) How long does it take stone to reach maximum height? b) How long is the stone in flight? c) What is the maximum height that the stone reaches? d) What is the stone’s range?

12. Reading Passage
There are two key principles of projectile motion - there is a horizontal velocity that is constant and a vertical velocity that changes by 9.8 m/s each second. As the projectile rises towards its peak, it is slowing down (19.6 m/s to 9.8 m/s to 0 m/s); and as it falls from its peak, it is speeding up (0 m/s to 9.8 m/s to 19.6 m/s to ...). Finally, the symmetrical nature of the projectile's motion can be seen in the diagram above: the vertical speed one second before reaching its peak is the same as the vertical speed one second after falling from its peak. The vertical speed two seconds before reaching its peak is the same as the vertical speed two seconds after falling from its peak. For non-horizontally launched projectiles, the direction of the velocity vector is sometimes considered + on the way up and - on the way down; yet the magnitude of the vertical velocity (i.e., vertical speed) is the same an equal interval of time on either side of its peak. At the peak itself, the vertical velocity is 0 m/s; the velocity vector is entirely horizontal at this point in the trajectory. These concepts are further illustrated by the diagram below for a non-horizontally launched projectile that lands at the same height as which it is launched.