Vectors In Two Dimensions
What is the Equation of Pythagorean theorem?
A2+ B2= C2
Does X/horizontal go with tan, cos, or sin?
Cos
I will draw a set of vectors. If one is 10.2 meters/second and one is 4.5 meters/second. What is the value of the resultant vector?
14.7 meters/second
What path/shape does a horizontally launched item make?
Parabolic path/ parabola
What is the acceleration of a jellyfish falling off a building?
Gravity, -9.8 m/s2
Add these two vectors. What is the resultant? ( I will draw on board)
I will draw on board
Sarah climbs a spiral staircase that is 12 meters high and 2 meters wide from the base. What is the magnitude of her resultant displacement?
12.165 meters
Which way does a tailwind go with a plane?
with the plane, it speeds it up
What is the horizontal acceleration?
There is none
What is the vertical component of velocity at it's highest point?
zero
Subtract these two vectors from one another. What is the resultant of the vectors?
I will draw on board
What is the equation to figure out an angle or angle of incline?
tan-1(y/x) or tan -1( opposite/adjacent)
A plane has a velocity of 455 km/hr east relative to the air, and there is a headwind with a velocity of 22 km/hr west relative to the ground , What is the plane's velocity relative to the ground?
433 km/hr east
A ball thrown horizontally from an apartment balcony hits the ground in 8 seconds. If the horizontal velocity of the ball is doubled, how long will it take to hit the ground?
8 seconds, same amount of time
What degree do two angles have to be shot at to have the same range but different launch speeds?
90 degrees
If the resultant is 5 m and one leg is 2 m, how long is the other leg?
4.58 m
The acceleration in the y direction is 12 m/s2 and the resultant acceleration is 15 m/s2, what is the acceleration in the x direction?
9 m/s2
A boat is headed with a velocity of 16 meters/second toward the west with respect to the water in a river. If the river is flowing with a velocity of 3.1 meters/second in the same direction as the boat. What would be the magnitude of the boat's velocity?
19.1 meters/second
A container of water is knocked off a 10 meter high ledge with a horizontal velocity of 1 meter/second. Calculate the time it takes for the container to reach the ground.
1.43 seconds
If the vertical component of velocity for a projectile is 9.2 meters/second, what is its hang time?
1.87 seconds
What is the rhyme to remember with Tan, Cos, Sin? Write it down including the positions.
SohCahToa
Sin= opposite/hypotenuse
Cos= adjacent/hypotenuse
Tan= opposite/adjacent
In a waterpark, people walk a distance 25 meters up an inclined ramp before getting on a water slide. If the spot from where they start sliding down is located 9 meters above the water's surface, calculate the angle of the ramp with the horizontal.
21.1 degrees
A boat is headed due east across a river at a velocity of 25 meters/second with respect to the water. The velocity of the river current is 2.7 meters/second due north. What is the angle at which the boat will deviate from its original path?
6.2 degrees
A hot air balloon is moving at a speed of 10 meters/second in the +x direction. The balloonist throws a brass ball in the +x direction at a velocity of +4 meters/second with respect to himself. If the ball lands after 30 seconds, about how far does it land horizontally from the point at which it was released?
420 meters
At which launch angle does the projectile undergo the maximum horizontal displacement?
45 degrees