Physics/Dr. Lankar
Name: ________________ section: ______________: grade% (my spot!):
_______
given its components.
BACK
1) FILL THE BLANK. BANK : Y, x-component, vertical, X, horizontal, y-axis , y-component, resultant
Observe the picture below. Here is a vector R. R is the vector sum of the vector ______ and the vector _______.
In Physics, X is called the ______________ of the vector R because X is along the x-axis.
Y is called the ______________ of the vector C because Y is along the ___________.
In Physics, X is also called the _______________ component and Y the ______________ component.
R is the vector sum of X and Y and is also called the ______________. (that's what R stands for).
2)Let's find the components of R (1 square = 1 unit)
X = _________ units (along x-axis)
Y= _________ units (along y-axis)
3) Can you think of a way to find the magnitude of the resultant R ? Using your math skills ?
hint: you will have to use the square root key of your TI.
magnitude of R = _____________ units
4) Now we need to find the direction. THat is the angle between R and the x-axis.
First, let's do it geometrically. Extend R with your pencil and use your protractor to find the angle.
angle A = ____________ degrees
5) Now let's use Algebra. First let's find the slope of the line that contains the vector R.
Slope = ________ ( that is rise/run there is not unit, use Y and X of course)
This ratio Y/X as a special name in Math. It is called the tangent (TAN on the TI) of the angle A.
or TAN(A) = Y/X
6) Once you have the slope it is easy to find the angle A using your TI. We need to undo the tangent to extract A.
You are going to use the function TAN-1 First go to MODE and switch to DEGREE. (instead of RADIAN)
Then 2ND TAN-1 (Y/X)
You find A = ___________. Do you find the same angle as in 4) ?
7) your turn:
A) The components of a vector are X = 3cm and Y = 5cm
Find the resultant R and the direction of the vector. (so use the square root and TAN -1)
R = ______ cm @ __________
B) X= 24cm, Y = 80cm, R = _____ cm @ ______
C) X = 32cm, Y = 19 cm , R = _____ cm@ _______
8) Find the height H , above the ground, the kite is flying. Follow the step.
A) write the expression for tan (48) :
tan(48) = slope of the line going through the head and the kite.
Call Y the vertical leg of the right triangle. (that is the rise of the triangle)
B) Use your TI to find tan(48) = _____ (make sure the mode is DEGREE)
C) Solve the equation. solve for Y = __________ft
(hint: TAN(48) / 1 = Y / X , X is given, you are solving for Y, solve like a proportion, cross mulitply divide)
D) H = Y + 4 . solve for H = ___________ ft
9) An airplane flying at an altitude of Y= 30,000 ft is headed toward an airport. To guide the airplane to a safe landing, the airport's landing system
sends radar signals from the runway at an angle A of elevation. The plane is at a 10 degrees elevation.
How far is the plane (measured from the ground) from the airport runway (solve for X) ? you can use the steps
A) Call X the distance between the runway and the plane.
Find the slope of the line going through the runway and the plane.
slope = ___________ (hint : slope = TAN (angle), you should know it now)
B) slope = Y/X . you have Y, you have the slope, solve for X. solve like a proportion.
X= ____________ ft.
C) Find the distance runway to plane.
R = ______________ ft.
10) A ski slope at a mountain has an angle of 25.2 degrees. The vertical height of the slope is Y = 1808 feet.
How long is the ski slope ? X = __________.
11) The track of the Duquesne incline is about X= 800 feet long and the angle of elevation is 30 degrees.
How high does the Duquesne Incline rise ? Y= _____ ft
12) You are standing 75 meters (X=75) from the base of the Jin Mao Building in Shangai, china. You estimate that the angle of elevation to the top of the building is 80 degrees.
Make a sketch.
A) What is the approximate height Y of the building ? Y= ____ meters. convert to miles. Y = _____ miles (1 mile = 1600m)
B) What is the distance between you and your friend? R = ______ m (that is the hypotenuse R, use square root again)
13) To measure the width of a river you plant a stake on one side on one side of the river. directly across from a boulder.
You then walk X= 100 meters to the right of the stake and measure a 79 degrees angle between the stake and the boulder.
What is the width (Y ) of the river? Y= ______ m.
1) FILL THE BLANK. BANK : Y, x-component, vertical, X, horizontal, y-axis , y-component, resultant
Observe the picture below. Here is a vector R. R is the vector sum of the vector ______ and the vector _______.
In Physics, X is called the ______________ of the vector R because X is along the x-axis.
Y is called the ______________ of the vector C because Y is along the ___________.
In Physics, X is also called the _______________ component and Y the ______________ component.
R is the vector sum of X and Y and is also called the ______________. (that's what R stands for).
2)Let's find the components of R (1 square = 1 unit)
X = _________ units (along x-axis)
Y= _________ units (along y-axis)
3) Can you think of a way to find the magnitude of the resultant R ? Using your math skills ?
hint: you will have to use the square root key of your TI.
magnitude of R = _____________ units
4) Now we need to find the direction. THat is the angle between R and the x-axis.
First, let's do it geometrically. Extend R with your pencil and use your protractor to find the angle.
angle A = ____________ degrees
5) Now let's use Algebra. First let's find the slope of the line that contains the vector R.
Slope = ________ ( that is rise/run there is not unit, use Y and X of course)
This ratio Y/X as a special name in Math. It is called the tangent (TAN on the TI) of the angle A.
or TAN(A) = Y/X
6) Once you have the slope it is easy to find the angle A using your TI. We need to undo the tangent to extract A.
You are going to use the function TAN-1 First go to MODE and switch to DEGREE. (instead of RADIAN)
Then 2ND TAN-1 (Y/X)
You find A = ___________. Do you find the same angle as in 4) ?
7) your turn:
A) The components of a vector are X = 3cm and Y = 5cm
Find the resultant R and the direction of the vector. (so use the square root and TAN -1)
R = ______ cm @ __________
B) X= 24cm, Y = 80cm, R = _____ cm @ ______
C) X = 32cm, Y = 19 cm , R = _____ cm@ _______
8) Find the height H , above the ground, the kite is flying. Follow the step.
A) write the expression for tan (48) :
tan(48) = slope of the line going through the head and the kite.
Call Y the vertical leg of the right triangle. (that is the rise of the triangle)
B) Use your TI to find tan(48) = _____ (make sure the mode is DEGREE)
C) Solve the equation. solve for Y = __________ft
(hint: TAN(48) / 1 = Y / X , X is given, you are solving for Y, solve like a proportion, cross mulitply divide)
D) H = Y + 4 . solve for H = ___________ ft
9) An airplane flying at an altitude of Y= 30,000 ft is headed toward an airport. To guide the airplane to a safe landing, the airport's landing system
sends radar signals from the runway at an angle A of elevation. The plane is at a 10 degrees elevation.
How far is the plane (measured from the ground) from the airport runway (solve for X) ? you can use the steps
A) Call X the distance between the runway and the plane.
Find the slope of the line going through the runway and the plane.
slope = ___________ (hint : slope = TAN (angle), you should know it now)
B) slope = Y/X . you have Y, you have the slope, solve for X. solve like a proportion.
X= ____________ ft.
C) Find the distance runway to plane.
R = ______________ ft.
10) A ski slope at a mountain has an angle of 25.2 degrees. The vertical height of the slope is Y = 1808 feet.
How long is the ski slope ? X = __________.
11) The track of the Duquesne incline is about X= 800 feet long and the angle of elevation is 30 degrees.
How high does the Duquesne Incline rise ? Y= _____ ft
12) You are standing 75 meters (X=75) from the base of the Jin Mao Building in Shangai, china. You estimate that the angle of elevation to the top of the building is 80 degrees.
Make a sketch.
A) What is the approximate height Y of the building ? Y= ____ meters. convert to miles. Y = _____ miles (1 mile = 1600m)
B) What is the distance between you and your friend? R = ______ m (that is the hypotenuse R, use square root again)
13) To measure the width of a river you plant a stake on one side on one side of the river. directly across from a boulder.
You then walk X= 100 meters to the right of the stake and measure a 79 degrees angle between the stake and the boulder.
What is the width (Y ) of the river? Y= ______ m.
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