CP Modified Pythagorean Theorem and Resultant Vector

The Pythagorean Theorem

The Pythagorean Theorem is used to find the unknown side measure in a right triangle. You may remember the Pythagorean Theorem from Geometry.

Multiple Choice

The following is the use of Pythagorean Theorem EXCEPT one;

• To determine the length and the direction of the resultant vectors.

• To find the length of a right triangle's sides.

• To combine the resultant of vectors in one dimensional.

• To add together two vectors at right angles.

Poll

The formula for the Pythagorean Theorem is below. Does this formula seem familiar to you?

 $a^2+b^2=c^2$  

• Yes!

• A little bit

• Not at all!

Parts of a Right Triangle

• Hypotenuse - Side across from (opposite) the right angle

• Legs - The other 2 sides

Multiple Choice

see image: Which is TRUE of about HYPOTENUSE?

• Longest side of a triangle

• Side across from the right angle

• Both a and B

In this triangle, the side labeled 65 is the hypotenuse because it is opposite the right angle. 

Multiple Choice

Which side is the hypotenuse in this right triangle?

• 5

• 12

• 13

Multiple Choice

(see image) Find the Resultant Displacement, d_R

• .5 km, South West

• 5.0 km South East

• 50.0 km South West

• 50.0 km South East

Multiple Choice

 $R_d\ =\ \sqrt{A^{2\ }}+\ B^2$  

(see image for the values) Find the RESULTANT of the DISPLACEMENT Vectors.

• 1.0 m, North West

• 5.0 m, North West

• 10 m, North West

• 50 m, North West

Multiple Choice

Word problem: Paul sprinted 120 meters east and then sprinted 40 meters west. What is his resultant DISPLACEMENT?

• 160 meters west

• 160 meters east

• 80 meters west

• 80 meters east

Multiple Choice

Riley drove his car 40 m/s east and was blown by a wind of 8 m/s south. What is his RESULTANT VELOCITY?

• 43 m/s, south east

• 40.8 m/s, south east

• 42 m/s, south east

• 44.7 m/s, south east

Multiple Choice

Bikers paddled 55 meters north and then 20 meters west. What is their RESULTANT DISPLACEMENT?

• 58.5 m north west

• 51.2 m north west

• 3422 m north west

• 61 m north east

Multiple Choice

A helicopter flies 25 m/s/s East and decelerates at 5 m/s/s Southward before coming to a stop. What is the MAGNITUDE of the RESULTANT ACCELERATION?

• 15.5 m/s/s South East

• 18.5 m/s/s Southward

• 25.5 m/s/s South East

• 35.5 m/s/s East of South

Multiple Choice

see image: Which is the most appropriate representation of the Resultant of Vectors A, B, and C?

Multiple Choice

Find the Resultant of the 2-FORCE VECTORS. ( see image)

 $R_{f\ }=\ \sqrt{A^{2\ \ }+\ B^2}$  

• 1.3 N North East

• 13 N North East

• 130 N North East

• 1,300 N North East

Multiple Choice

 $V_{R\ }=\ \sqrt{A^2\ +\ B^2}\$  Find the RESULTANT of the 2 VELOCITY VECTORS. (see image)

• 17 m/s North East

• 1.7 m/s North West

• .17 m/s North East

• .017 m/s North West

Multiple Choice

The following quantities are VECTOR quantities EXCEPT

• Mass

• Acceleration

• Velocity

• Force

Multiple Choice

Vector quantity has both magnitude and direction.

• True

• False

Open Ended

How well do you understand Pythagorean Theorem in finding the magnitude of the RESULTANT VECTOR?