Quiz 3 Flashcards
Gravity causes a projectile to move in a (blank) path that is symmetric about the (blank)
parabolic
apex
What are the 2 different types of projectile motion?
1. Object acting as projectile
(Basketball, baseball, football, shot put, hammer, discuss, javelin, volleyball, tennis ball, arrow (archery)
(High jump, long jump, gymnastics, figure skating, diving, ski jumping)
What are the 3 main variables we manipulate in projectile motion?
- Flight distance
- Flight time
- Maximum height
Why do we always break the motion into X and Y components (displacement, velocity, acceleration)?
- Because they are INDEPENDENT
- Because the vertical component is influenced by gravity (x) and the horizontal(y) component is not à Allows us to use different equations
- both are vectors.
Takeoff velocity often given as projected (blank) with corresponding (blank)
(ie. Ball was projected at 10 m/s at 30° to the horizontal)
vector
angle
What are the 2 perpendicular components of a velocity?
Vx = horizontal component
Vy = vertical component
If the angle between 2 known-length vectors is (blank), you can use pythagorean theorem to find your unknown
90 degrees
What is the formula for pythagorean theorem?
R2 = P2 + Q2
(blank) = Longest side but shortest distance
between x and y points
hypoteneuse
sin = (blank)
cos = (blank)
tan = (blank)
opp/hyp
adj/hyp
opp/adj
Remember that the motion of a body is influenced only by (blank) (in the vertical direction).
Therefore the ONLY acceleration that the body experiences is a vertical acceleration due to gravity of (blank) in the (blank) direction
gravity
9.81 m/s2
downward
Horizontally, (blank) must be zero, since no forces act in this direction (ignore air resistance)
SO… Equation for constant (blank) applies
sfx = six + vixt
- Where sfx and six are the (blank) and (blank) displacements in the x direction
- vix is the initial and (blank) velocity in the x direction
- t is the time component
acceleration
horizontal motion
final
initial
constant
Equations for vertical component of projectile motion:
Use the equations for constant acceleration, replacing (blank) with (blank) (-9.81 m/s2)
a
g
What are the 3 factors that influence projectile trajectory?
Projectile angle
Projectile speed
Relative height of projection
(projection height - landing height)
What is the optimal angle of projection for the most distance?
45 degrees
How are 15/75 degree and 30/60 degree projection angles related?
They will have the same horizontal distance as they have the same difference between them and 45 degrees
How does projectile speed affect horizontal distance?
An increase in speed results in an increase in object displacement, assuming the same projection angle
Angle of projection θ dictates magnitude of the X and Y components.
angle < 45 then (blank)
angle = 45 then (blank)
angle > 45 then (blank)
Vx > Vy (X bigger)
Vx = Vy (same)
Vx < Vy (Y bigger)
Relative projection height :
difference between (blank) height and (blank) height
projection
landing
*Relative projection height = 0
(Release = Landing)
* (blank)
* (blank)
soccer
golf drive on level ground
*Relative projection height > 0
(Release lower than Landing)
* (blank)
* (blank)
golf shot onto elevated green
basketball free throw
- Relative projection height < 0
(Release higher than Landing) - (blank)
- (blank)
soccer throw in
shotput
What is the best projection angle for maximum height?
90 degrees
Relative projection height greater than 0
optimal projection angle of (blank)
less than 45 degrees
Relative projection height equal to 0
optimal projection angle of (blank)
45 degrees
Relative projection height less than 0
optimal projection angle of (blank)
greater than 45 degrees
What is the optimal angle for maximum projection speed?
45 degrees
If Hprojection = 0 (ie. Hrelease = Hlanding)
the optimal release angle is (blank)
45 degrees
Horizontal velocity is determined by
1. (blank)
2. (blank)
projection speed
projection angle
Vertical velocity is determined by
1. (blank)
2. (blank)
projection speed
projection angle
Maximum height is determined by
1. (blank)
2. (blank)
vertical velocity
projection height
Flight time is determined by
1. (blank)
2. (blank)
3. (blank)
vertical velocity
projection height
final height
Flight distance is determined by
1. (blank)
2. (blank)
horizontal velocity
flight time
(blank) axis (Sagittal plane):
divides the body into left and right halves
(blank) axis (Frontal plane):
divides the body into front and back halves
(blank) axis (Transverse plane):
divides the body into top and bottom halves
mediolateral
anterioposterior
vertical
What are 3 ways to measure angular displacement?
Can be measured using
*Revolutions (r)
*Degrees (deg)
*Radians (rad)
What are two scenarios where revolutions are used as a measurement of angular displacement?
Used in sport description
- Diving/Gymnastics/Figure Skating
* full twisting one and a half
* inward two and a half
2.Cycling
* rpm
What is the ratio of a degree to a revolution?
what are 3 uses of degree as a measurement?
Smaller unit (1/360th of a revolution)
Widely used in everyday life and sport
1. loft of the club
2. angle of release
3. segment description
How big is a radian compared to a degree?
What is the definition of a radian?
Much smaller value than degrees
Radian: Ratio of arc length to the radius of circle
What is the equation for a radian?
Theta = s/r
Where:
Theta = angle
s = arc length
r = radius
if arc length (s) = length of radius (r)
then angle (ϴ) = 1 radian
The number of radians in a semicircle = (blank)
The number of degrees in a semicircle = (blank)
Therefore 1 rad = 180 deg/π = (blank)
pi
180
57.3 degrees
Knowing that the circumference of a circle is:
*(blank) degrees
*(blank) rad
*(blank) revolution
360
2
1
What is the angular displacement of 96 degrees expressed in radians
1.675
Express a displacement of 0.82 radians in degrees
46.986
What is the equation for angular velocity?
ω = Δϴ/ Δt = (ϴf - ϴi ) / ( tf - ti )
ω = angular velocity (omega)
ϴ = angular displacement in radians
∆t = time interval in seconds
What is the equation for angular acceleration?
α = Δω / Δt = (ω f - ω i ) / ( tf - ti )
α = acceleration (alpha)
ω = angular velocity in radians/second
Δt = time interval in seconds
A figure skater performs a triple twisting jump. She rotates around her longitudinal axis three
times while she is in the air. The time it takes to complete the jump from takeoff to landing is
0.8 seconds. What was Michelle’s average angular speed in twisting for this jump?
(blank) rev/s
(blank) degree/s
(blank rad/s
3.75 rev/s
1350 degree/s
23.6 rad/s
ω= ∆θ/ ∆t
ω = 3revs/0.8sec
ω = 3.75rev/s
Or
ω = 1080º/0.8sec = 1350º/s
Or
ω = 18.8rad/0.8sec = 23.6rad/s
What is the angular acceleration of a person who increases her angular velocity from 5.50 to 9.00 rad/s in 3.00s?
(blank) rad/s2
1.167 rad/s2
α = 9.0-5.5 / 3.0
α =1.167 rad/s2
Many sports use angular (blank) to increase the linear (blank) of an implement:
ie., hammer throw, discus, golf, baseball, almost any projectile activity
motion
velocity
The (blank) the radius of rotation (r), the (blank) the linear distance or arc distance (s) travelled by a point on a rotating body.
larger
greater
What is the equation for linear displacement?
s=(r)(theta)
where:
*s = linear displacement of the point of interest
*r = radius of rotation
*theta = angular displacement of the rotating body
(MUST BE in radians (57.3 degrees)
A baseball player swings a bat at a fast ball. Consider the handle of the bat where the hands grip it to be the fulcrum. The bat is 0.5m from the handle to the top of the bat. The start angle of the swing is 170º and the angle at which the ball is hit is 90º.
A. What is the angular distance traveled by the bat?
B. What is the linear distance traveled by the end of the bat?
A.
Angular distance (ϴ) = 170̊– 90̊ = 80̊
Change 80 deg to rad = 1.40
B.
s = (r)(theta)
s = 0.5*1.40rad
s=0.7m
Instantaneous linear velocity occurs at a (blank) to the circular path of the point.
tangent
§If the object was released from its (blank) motion, it would travel on a tangent
line from that point out with an initial linear (blank).
angular
velocity