Lecture 5 - projectile motion Flashcards
What is projectile
Any object in free fall and affected only by gravity and air resistance
Trajectory is
Flight path of projectile (the arch)(predicable motion)
Release is when
Objects begins projectile motion
Apex is
The highest point in trajectory
Projectiles have…?
Velocity
Horizontal component for projectile from when we release it until it stops will be changing or constant?
Constant
The vertical component will be constant or changing
Change
What affects the vertical displacement/apex/ depends on
Vertical velocity
What depends on projection angle
Magnitude of projectile motion
The x component and y component of projectile motion are dependent or independent?
Independent of each other (separate)
Airborne motion is always these 3 rules
- Parabolic path of CoM
- Constant horizontal velocity
- Constant vertical acceleration
Gravity influences Vx or Vy
Vy
As the object is moving up, Vy is
Decreasing
When the object is at apex the Vy is going to be
Zero
When object is moving down, the Vy is going to be
Increasing
When object is going up the gravitational force is going to be
-9.81 m/s^2
When object is going down the gravitational force is going to be
9.81 m.s^2
Trajectory of centre of mass (CoM) of projectile is always
Parabolic regardless of motion of body seamen’s
Trajectory of centre of mass (CoM) of projectile is always
Parabolic regardless of motion of body segments
What are the 3 different factors that can change projectile motion and how far the object moves
- projectile height of release (relative height)
- projection angle (angle of release)
- projectile velocity (velocity of release)
Anything that is being thrown at a higher place, the object will have. A longer or shorter time in the air
Longer flight time
If we have a constant projectile velocity and a constant angle but we alter projectile height, what will happen?
Increase flight time = increase horizontal displacement
Horizontal displacement is dependent on how long
You spend in the air (flight time) ex. At longer period of time but same velocity will result in a longer distance
If release height is the same as landing height will foes it mean? Add pic
Time to apex= time to land
Vy release = Vy landing
Release height > landing height ad pic
Time of apex < time to land
Release height < landing height add pic
Time to apex > time to land
Vy release > Vy landing
If the projection angle is 90 (shot straight up) all the velocity would be on
Vy and Vx=0
Projection angle influences shape of ______
Projectile’s trajectory
If projection angle is between 0 and 90 it will create
Parabolic trajectory will have every things listed for projectile motion
If projection angle = 0, if the release height is> landing height will have
1/2 parabola trajectory and Vy initial = 0
If you had the same weight of bricks and feather which will drop first? Why?
Both fall the same time because air resistance is zero, gravity will affect the same way since they are falling from the same height
If you want to maximize your vertical displacement you want to make your angle as?
Steep as you can closer to 90 degree
Maximize horizontal displacement you want to make your angle depend on
Optimal angle (height of release)
For projection height
Release height = landing height —> optimal angle is
Release heighT>landing height —> optimal angle is
Release heighT < landing height —> optimal angle is
45
<45
> 45
Why is 45 the optimal angle
By having the same release height and landing height and the angle is 45 it will maximize flight time and horizontal velocity
Projectile velocity determines
Magnitude of vertical and horizontal displacement
What is the most important factor in changing projectile motion
Projectile velocity
A potato cannon has a fixed angle of 50 degree relative to the ground. How can we alter the firing distance (displacement over time) if the angle is fixed?
Cannot move or change height,
We can increase the projectile velocity or
A cannon with a fixed to the ground fires with a velocity of 1000m/s. How do we alter this cannon’s firing distance?
We have a fixed height and velocity
Alter the projection angle to optimal angle
Example needing maximize vertical displacement?
High jump, pole vault (steep projection angle)
Maximize horizontal displacement?
Long jump, triple jump (small projection angle)
Example for when release ht=landing ht —> optimal projection = 45
Kick.a soccer ball for max horizontal displacement
Example for when release ht>landing ht —> optimal projection < 45
Throwing a baseball for max horizontal displacement
Example for when release ht optimal projection > 45
Chip into an elevated green (golf)
A cannon fires with a fixed angle of 50 and fixed velocity of 1000m/s. How do we alter the cannon’s firing distance?
Alter projectile height and increase it = increase horizontal displacement
Changing projectile height (increasing it) will only affect
Time of object going down
Total time can help figure out your
Horizontal displacement
Time total is
Time up + time down
Flight time is influenced by
Vy intital and projectile height
Horizontal displacement is influenced by
Vx time in air
Vertical displacement is influenced by
Vy initial, projectile height
Trajectory is influenced by
Initial velocity (magnitude), projection angle and projectile height
When analyzing horizontal components the Acceleration is 0
- Vf=Vi+at —> vf=vi
- D=Vit +1/2 a^2 -> d=Vit
- Vf^2 = Vi^2 +2ad —> Vf2=Vi2
Anazlying when dropping a ball from a given height its a=-9.81 m/s^2
Vi=0
- Vf=Vi+at —> vf=at
- D=Vit +1/2 a^2 -> d=1/2at^2
- Vf^2 = Vi^2 +2ad —> Vf2=2ad
Analyzing vertical components when at apex
- Vf=Vi+at —> 0=Vi+at
3. Vf^2 = Vi^2 +2ad —> 0=.Vi2+2ad
Time up Vy=Vf is
Zero
When time down, Vy=Vi is
Zero
A ball is thrown in the air with an initial velocity of 30 m/s and a horizontal velocity of 5 m/s. What was the maximal height reached by the ball? Vertical displacement
Add pic
A football is kicked with the initial horizontal velocity of 18 m/s and a flight time of 2s. How far will the ball travel?
Add pic
A ball is kicked with the initial horizontal velocity of 35 m/s and a vertical velocity of 10 m/s. how far will the ball travel
Add pic
A soccer player kicks a ball. The ball leaves the foot at a 23° angle relative to the horizontal, with a velocity of 58 m/s. The ball is in the air for 0.83 seconds.
A) What is the ball’s vertical and horizontal velocity immediately after release?
B) What is the ball’s max horizontal displacement?
C) What is the ball’s vertical velocity at max vertical displacement?
D) What is the ball’s max vertical displacement?
E) What is the ball’s horizontal velocity just prior to contact time?
F) What is the ball’s vertical velocity just prior to contact time?
Add pic
You hit a golf ball. The ball leaves the ground at
25 m/s at an angle of 60° from the ground.
A) What is the maximum height the ball reaches?
B) How much time does it spend in the air?
C) How far does the ball travel?
Add pic
You hit onto an elevated green, which has a rise of 3m.
You hit the ball at 45 m/s at an angle of 55°. A) How high does the ball travel?
B) How much time does it spend in the air?
C) How far does the ball travel?
Add pic
When the optimal angle is > 45 what happens
Release height < landing height
Optimal angle is < 45
Release height > landing height
When optimal angle is 45 what happens
Release height = landing height
