3. Vectors

Tom is climbing a 3.0-m-long ladder that leans against a vertical wall, contacting the wall 2.5 m above the ground. His weight of 680 N is a vector pointing vertically downward. (Weight is measured in newtons, abbreviated N.) What are the components of Tom's weight parallel and perpendicular to the ladder?

A jet plane taking off from an aircraft carrier has acceleration a = ( 15 m/s², 22° above horizontal). What are the horizontal and vertical components of the jet's acceleration?

Jack and Jill ran up the hill at 3.0 m/s. The horizontal component of Jill's velocity vector was 2.5 m/s. What was the vertical component of Jill's velocity?

A cannon tilted upward at 30° fires a cannonball with a speed of 100 m/s. What is the component of the cannonball's velocity parallel to the ground?

Let $\overrightarrow{B}$ = (5.0 m, 30 degrees counterclockwise from vertically up). Find the x- and y-components of $\overrightarrow{B}$ in each of the two coordinate systems shown in FIGURE EX3.21.

Vector A is 2.80 cm long and is 60.0° above the x-axis in the first quadrant. Vector B is 1.90 cm long and is 60.0° below the x-axis in the fourth quadrant (Fig. E1.35). Use components to find the magnitude and direction of A - B In each case, sketch the vector addition or subtraction and show that your numerical answers are in qualitative agreement with your sketch.

Draw each of the following vectors. Then find its x- and y-components. $v=(440\text{m/s},{30}^{\circ }\text{below the positive }x\text{-axis})$

Vector A has y-component A_y = +9.60 m. A makes an angle of 32.0° counterclockwise from the +y-axis. (a) What is the x-component of A? (b) What is the magnitude of A?

An airplane is traveling 815 km/h in a direction 41.5° west of north (Fig. 3–40). Find the components of the velocity vector in the northerly and westerly directions.

Compute the x- and y-components of the vectors A, B, C, and D in Fig. E1.24.

Jack and Jill ran up the hill at 3.0 m/s. The horizontal component of Jill's velocity vector was 2.5 m/s. What was the angle of the hill?

Kami is walking through the airport with her two-wheeled suitcase. The suitcase handle is tilted 40° from vertical, and Kami pulls parallel to the handle with a force of 120 N. (Force is measured in newtons, abbreviated N.) What are the horizontal and vertical components of her applied force?