Projectile Motion & Vectors
Projectile motion is the motion of an object in flight including the impact of gravity The curved flight of a football or
baseball seen during a game is an excellent example of projectile motion
Understanding Projectile Motion To understand projectile motion, it is
easiest to break the motion down into motion in two directions- x and y
We did this last unit with the marble/ramp lab The marble rolling down the ramp at an
angle was moving in the x direction (horizontally) and y direction (vertically)
Marble/Ramp Vectors
Marble rolls down
the ramp
Marble travels in
the x direction
Marble travels in
the x direction
Vectors A vector is a drawing showing
direction and magnitude Magnitude is the measure of how
large something is Ex. Magnitude 4.5 earthquake, 55 mph
A vector sounds a lot like a velocity, and vectors are frequently drawn to represent velocities
Drawing vectors A vector is drawn with an arrow
pointing the direction of the vector The arrow should be drawn to a
scale length Perhaps 1 cm line represents 10m/s
Vector examples
45 mph east
9.8 m/s2
down
What good are they? Vectors give a visual
representation of the directions of motion
Vectors can work together to show us what the net result will look like
Vectors can be added to calculate the net result (resultant vector)
A Thrown ball
The quarterback throws the ball at 9 m/s at a 30° angle (to horizontal)
9 m/s
A Thrown ball
The ball moves in the x direction
9 m/s
The ball moves in the y direction
Vectors can add together Vectors can work together to
describe the final, or resultant, vector
For example A boat traveling down a river gets to go
faster because the river “pushes” the boat faster
A boat traveling up river goes slower because it has to go against the river
River Trip
Boat travels 35 mph up river
River travels 10 mph downstream
Result – boat travels 25 mph up river
River Trip
Boat travels 35 mph down river
River travels 10 mph downstream
Result – boat travels 45 mph down river
Vectors can add in any direction!
Boat travels 35 mph across the river
River travels 10 mph downstream
Resultant Boat travels 35 mph across the river
River travels 10 mph downstream
Resultant
Calculating the vectors
The y vector = sin of angle X velocity sin(30)*9 m/s Vy = 4.5 m/s
9 m/s
30°
When the football is thrown, it goes upwards at 4.5 m/s
Calculating the vectors
The x vector = cos of angle X velocity cos(30)*9 m/s Vx = 7.79 m/s
9 m/s
30°
When the football is thrown, it goes down field at 7.79 m/s
Practicing vectors
Find the x and y vectors for the football thrown as shown
12 m/s
50°
Vx = cos(50)*12 m/sVx = 7.71 m/sVy = sin(50)*12 m/sVy = 9.19 m/s
Using vectors
A projectile has a curved path as it flies It spends half of its flight time on the
way up, and half on the way down
12 m/s
50°
Using vectors
Let’s find how long it takes for the ball to reach the top of its trajectory, or curved path
12 m/s
50°
How long does it fly? First, we know it goes up at 9.19 m/s Second, we know velocity at the top of the
trajectory is 0 m/s Third, we know that the upwards velocity
decreases at 9.8 m/s2 due to gravity
12 m/s
50°
How long does it fly? Use the formula
a=(Vf-Vo)/t -9.8 m/s2=(0 m/s-9.19 m/s)/t -9.8 m/s2=(-9.19 m/s)/t t=(-9.19 m/s)/(-9.8 m/s2) t=.94 seconds to fly up ttotal = 2*.94 ttotal = 1.88 seconds
12 m/s
50°
How far it fly? First, we now know the time it flies (1.88 seconds) Second, we know the horizontal velocity (vx) = 7.71 m/s Use the formula v=d/t
7.71 m/s = d/1.88 seconds d=7.71 m/s * 1.88 s d = 14.49 m
12 m/s
50°
Try another (simpler) A marble rolls off a table 1.5 m high with a
velocity of 5 m/s How far from the table will it hit the floor? Formulas
d=1/2at2
v=d/t
5 m/s
1.5 m
Try another (simpler) Use d=1/2at2
to find time it drops (and flies away from the table) 1.5 m = ½(9.8 m/s2)(t2) 3m/(9.8 m/s2)= t2
t2 = .31 seconds2
t =.56 seconds Find the distance
5 m/s=d/.56 seconds 2.8 m = d
5 m/s
1.5 m