CH3 AND TRIG Flashcards
What is your favorite class?
Physics.
What does SOH CAH TOA stand for?
sin angle= opp/hyp cos angle = adj/hyp tan angle = opp/adj
How to solve for x: trig X = B/C
UNTRIG: trig-1 (B/C) = x
How to solve for x: trig A = X/C
SLIDE: C trig angle = x
How to solve for x: trig A = B/X
SWITCH: B/trig angle = x
How to solve triangles when there are no angles given?
PYTHAGOREAN THEOREM (or law of sines)
What are other names for UN-TRIG?
arc trig, inverse trig, trig ^ -1
What to the interior angles of a triangle add up to?
180 degrees, since a right triangle already has a 90 degree angle, the other two angles are complementary (add to 90)
What do the two smaller angles in a right triangle add up to?
90
What do you call angles that add to 90?
Complementary
What angle of elevation will give the same horizontal range as a 20 degree launch?
A 70 degree launch. Complementary angles go the same horizontal distance
sin 70 = cos __
20
cos 50 = sin __
40
sin 50 / cos 50 = tan ____
50
sin m = cos ___
90-m
cos g = sin ____
90-g
sin f / cos f = tan ___
f
How far does a dropped object fall in 1sec, 2sec, 3sec, 4sec, 5sec? hint: use d=5t^2
5m, 20m, 45m, 80m, 125m.
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. The vertical changes (accelerates) and the horizontal is constant.
Discuss the vertical component of a thrown baseball
CHANGING VELOCITY. The vertical component is impacted by gravity, so always changing by 10m/s per second.
Discuss the horizontal component of a thrown baseball.
SAME VELOCITY THE WHOLE TIME. Because we ignore air resistance, we assume that the baseball moves at constant velocity horizontally
How can you think about the horizontal component of velocity to help understand it?
GROUND SHADOW, for Vx, horizontal, imagine the sun straight above and visualize the speed of the shadow cast on the ground. the speed of the shadow is the horizontal speed.
How can you think about the vertical component of velocity to help understand it?
WALL SHADOW, For Vy, the vertical speed, imagine a huge spotlight behind where the projectile is being launched from, pointing in the direction of the projectiles path. Also imagine a wall just beyond it. the speed of the shadow of the ball on that wall is the vertical speed.
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)
If you know horizontal and vertical component, how do you find angle??
tan -1 (opp/adj)
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 (like a seagull)
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
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 don’t change.. horizontal velocity stays constant.
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). JUST THE VERTICAL becomes zero, but it is still moving horizontally!
what is a “horizontal range?”
the distance a projectile travels along the ground (horizontally)
What is an interesting fact about horizontal ranges of projectiles and angles aside from 45 is the furthest?
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. the velocity is ALL HORIZONTAL there because the vert v is zero.
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. The velocity at the top, then, is just the horizontal speed. You can visualize this by imagining a ball thrown straight up.. it stalls at the top for a split second.
What is the vertical velocity component of a projectile at the highest point?
ZERO
What is the horizontal velocity component of a projectile at the top?
The same as it is everywhere. The horizontal speed doesn’t change
What is the vertical acceleration of a projectile at the highest point?
10m/s2. A projectile is accelerating towards earth at 10 meters per second each second along the entire path.
What is the horizontal acceleration of a projectile at the top?
ZERO. It does not accelerate horizontally, it stays the same speed
What is the horizontal acceleration of a projectile as it flies through the air?
ZERO. It does not accelerate horizontally, it stays the same speed
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?
250 miles (400 km) From here to Burlinton VT, at about the canadian border!
SATELLITES: How fast does the international space station move?
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/s, air resistance makes it impossible. things would burn up (like shooting stars do)
