QQ: Finish Page 121 1-4: Sketch & Label Diagrams for all problems. Show all work using the problem solving sets used in class. No work = No credit Prepare to share your answers with the class.

Page 104 Practice Problems 28-31 DUE TODAY Page 104 Practice Problems 28-31 And page 112: 41 – 47

Today’s Objective: I can use vector components to solve problems.

When its not 900, use R2= A2 + B2 – 2AB(COSӨ) Remember: The Pythagorean Theorem can only be used with right triangles. When its not 900, use R2= A2 + B2 – 2AB(COSӨ)

It seems natural to use vectors when we are talking about movement, distance, and direction. But they are also helpful in calculating the magnitude and direction of both field and contact forces.

In order to solve problems with vectors, it is helpful to be able to break a vector down into its component vectors. Component vectors show the horizontal and vertical vectors that are added together to get the vector in question as a resultant. Vx + Vy = V

Then add the x-component and the y-component of the vector. Create a coordinate grid to help you see directions and angles from the horizontal plane. The grid can be tilted if that helps your picture in any way. Then add the x-component and the y-component of the vector.

We know angle and hypotenuse. Find adjacent side by using Cos 43. 10 m 43o 7.3 m We know angle and hypotenuse. Find adjacent side by using Cos 43. Cos 43 = adj/hyp Cos 43 = x/10 7.3 m = x

We know angle and hypotenuse. Find opposite side by using Sin 43. 10 m 6.8 m 43o 7.3 m We know angle and hypotenuse. Find opposite side by using Sin 43. Sin 43 = opp/hyp Sin 43 = x/10 6.8 m = x

Break this vector down into its x- and y- components. 13 m/s 68o 112o 4.8 m/s Break this vector down into its x- and y- components. Add a coordinate system. Draw the tail to head vectors. Calculate supplemental angle measure Calculate x-component using: Cos 68 = adj/hyp = x/13 13 cos68 = 4.87

Calculate the y component using sin 68: Sin 68 = opp/hyp = x/13 13 m/s 12.1 m/s 68o 112o Calculate the y component using sin 68: Sin 68 = opp/hyp = x/13 13 Sin 68 = 12.1 Now we have some background about this vector and ways we can use it in a problem. 4.8 m/s

Mac drives his car 6.0 km, North before making a right hand turn and driving 6.0 km to the East. Finally, he makes a left hand turn and travels another 2.0 km to the north. What is the magnitude of the overall displacement? Create a diagram of his travels. Make sure the vectors are proportional. 2 6 ? 6

There are no obvious right triangles with the resultant vector as the hypotenuse. But vector addition is commutative and order doesn’t matter. So rearrange the vectors to create a right triangle. Notice the resultant Vector remained the Same magnitude & Direction. 2 6 ? 6

There are no obvious right triangles with the resultant vector as the hypotenuse. But vector addition is commutative and order doesn’t matter. So rearrange the vectors to create a right triangle. Solve for the resultant Using the Pythagorean Theorem. 6 8 ?

Treat east as +X and north as +Y. Add the following two vectors via the component method: A is 4.0 m south and B is 73 m northwest. Treat east as +X and north as +Y. B = 7.3m A = 4.0m

Add the following two vectors via the component method: A is 4 Add the following two vectors via the component method: A is 4.0 m south and B is 73 m northwest. B = 7.3m A = 4.0m

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