Vectors have both _____ and _____
magnitude and direction
Describe magnitude and direction.
Magnitude answers “how much?” and direction answers “which way?”
What is difference between vector and scalar quantities?
Vectors have magnitude and direction, so combining them is tricky. Scalars have magnitude only, so they can be easily added, subtracted, multiplied and divided.
Give examples of vector quantities.
Velocity, acceleration, and force.
Give examples of scalar quantities.
mass, time, volume, area.
A thrown baseball has has two velocity components. Describe them
A vertical component and a horizontal component. The vertical component and the horizontal components are independent, so they do not act on eachother.
Discuss the vertical component of a thrown baseball
The vertical component is impacted by gravity, so always changing by 10m/s per second. It changes the same as something thrown straight up in the air.
Discuss the horizontal component of a thrown baseball.
Because we ignore air resistance, we assume that the baseball moves at constant velocity horizontally.
For projectiles, how can we think of the horizontal and vertical speeds? (shadows)
We can imagine SHADOWS. For Vx, or the horizontal speed, imagine sun above and picture the movement of the shadow of the ball moving on the ground. For Vy, imagine a bright light shining directly behind the motion towards a wall. Now imagine the movement of the shadow of the ball along the wall, that would be the vertical component.
If we know the horizontal and vertical component of a thrown baseball, how can we find the initial velocity?
Use the PYTHAGOREAN THEOREM v = sqrt (h squared + v squared)
Suppose you know the hypotenuse and the measure of an angle, and want to find the side close to the angle, how do you do it? how do you find the close side?
hypotenuse x COS (angle) [cosine finds the close side]
Suppose you know the hypotenuse and the measure of an angle, and want to find the side across from the angle, on the opposite side?
hypotenuse x SIN (angle) [sin finds opposite side]
The vector given is usually the ________ of the triangle.
hypotenuse
Plane traveling north at 300 km/h hits headwind of 100km/h. What is landspeed? airspeed?
landspeed is 200km/h and airspeed is still 300km/h
Special triangles?
3-4-5 (37-53-90), 1-1- sqrt 2 (45-45-90), 1-sqrt 3- 2 (30-60-90)
What are the 3-4-5 right triangle angle measures
ABOUT: 37-53-90. across from those sides respectively)
what are the angle measures of a 1-1-root 2 triangle?
45 -45- 90 across from those sides respectively)
what are the angle measures of the 1- sqrt 3- 2 triangle?
30- 60- 90 (across from those sides respectively)
What are the side lengths of the 37-53-90 triangle?
3-4 and 5
What are the side lengths of the 45-45-90 triangle?
1, 1 and sqrt 2
What are the side lengths of the 30-60-90 triangle?
1, sqrt 3 and 2
A plane traveling north at 300 km/h with no wind: What is landspeed?
landspeed is 300km/h and airspeed is still 300km/h
A plane traveling north at 300 km/h airspeed hits southerly wind of 50 km/h. What is landspeed?
250 km/h
A plane traveling north at 300 km/h airspeed hits southerly wind of 300 km/h. What is landspeed?
- It will look like it is standing still in mid-air
A plane traveling north at 300 km/h airspeed hits northerly wind of 50 km/h. What is landspeed?
350 km/h. The wind speed adds to groundspeed
A plane traveling north at 300 km/h airspeed hits easterly wind of 400 km/h. What is landspeed?
Landspeed is the diagonal of triangle with sides 300 and 400, using 3-4-5 triangle, the diagonal is 500km//h. The airspeed is still 300km/h
What is a clever way to look at projectile motion?
Imagining the projectile as a free falling object from different places along a straight diagonal line drawn at initial angle
If a bullet is shot horizontally at the exact time another is just dropped from the same height right next to it, which will land first (on flat surface)?
they will land at the same time
When drawing velocity vectors along the path of a projectile, what doesn’t change?
The horizontal vectors stay the same
When drawing velocity vectors along the path of a projectile, how does the vertical vector change?
Gravity impacts it. They become shorter on the way up, and ZERO at top, then get longer on the way down (pointing down) The velocity changes every second (10m/s each second). IT BECOMES ZERO AT THE TOP
what is a “horizontal range?”
the distance a projectile travels along the ground (horizontally)
What is an interesting fact about horizontal ranges and angles (when kicking a soccer ball or firing an arrow?)
complementary angles (angles that add to 90) have the same horizontal range. EXAMPLE: kicking a ball at 30 degrees will go the same distance as 60 degrees (neglecting air resistance. Shooting an arrow at 10 degrees will travel the same horizontal distance as one shot up at 80 degrees!!!
When is a projectile traveling the slowest?
At the top
Explain why a projectile is traveling slowest at the top
We know the horizontal component is always the same, so that will always be contributing, but the vertical component becomes ZERO at the top. You can visualize this by imagining a ball thrown straight up.. it stalls at the top for a split second.
What angle of elevation maximizes horizontal range?
45 degrees.
SATELLITES: How much does the earth curve over 8 km?
about 5 meters
SATELLITES: If an object falls at about 5 m in first second, and the earth curves about 5m every 8km. How fast would something have to travel horizontally to never hit the earth?
8km/s (neglecting air resistance)… now you orbit :)
SATELLITES: How far up is the international space station?
400 km (250 miles)
SATELLITES: How fast does the international space station move?
28,000 km/h about 8 km/s . (17,500 mph, about 5 miles per second)
SATELLITES: How many times does the international space station orbit the earth each day?
It circles the earth every 90 minutes, about 16 times a day!!
SATELLITES: Why do we have to be above earth’s atmosphere to orbit?
Traveling 5 miles in a second, or 8km, air resistance makes it impossible. things would burn up (like shooting stars do)
