Two-Dimensional Motion and Vectors. Chapter 2. Objectives 1. Distinguish between a scalar and a vector. 2. Add and subtract vectors by using the graphical method. 3. Multiply and divide vectors by scalars. Vectors, Shmectors. Vectors, Schmectors.
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1. Identify appropriate coordinate systems for solving problems with vectors.
2. Apply the Pythagorean Theorem and tangent function to calculate the magnitude and direction of a resultant vector.
3. Resolve vectors into components using sine and cosine functions.
4. Add vectors that are not perpendicular.Vector, Schmector Operations
A plane travels from Houston, Texas to Washington, DC, which is 1540 km east and 1160 km north of Houston. What is the total displacement of the plane?Concept Check
Emily passes a soccer ball 6.0 m directly across the field to Kara. Kara then kicks the ball 14.5 m directly down the field to Luisa. What is the ball's total displacement as it travels between Emily and Luisa?Concept Check
An arrow is shot from a bow at an angle of 25° above the horizontal with an initial speed of 45 m/s. Find the horizontal and vertical components of the arrow's initial velocity.Concept Check
A truck drives up a hill with a 15° incline. If the truck has a constant speed of 22 m/s, what are the horizontal and vertical components of the truck's velocity?Concept Check
A plane flies 118 km at 15.0° south of east and then flies 118 km at 35.0° west of north. Find the magnitude and direction of the total displacement of the plane.Concept Check
A football player runs directly down the field for 35 m before turning to the right at an angle of 25° from his original direction and running an additional 15 m before getting tackled. What is the magnitude and direction of the runners total displacement?Concept Check
A plane travels 2.5 km at an angle of 35° to the ground and changes direction and travels 5.2 km at an angle of 22° to the ground. What is the magnitude and direction of the plane's total displacement?Concept Check
A cat chases a mouse across a 1.0 m high table. The mouse steps out of the way, and the cat slides off the table and strikes the floor 2.2 m from the edge of the table. When the cat slid off the table, what was its speed?Concept Check
A pelican flying along a horizontal path drops a fish from a height of 5.4 m. The fish travels 8.0 m horizontally before it hits the water. What is the pelican's speed?Concept Check
If the pelican in item 3 was traveling at the same speed but was only 2.7 m above the water, how far would the fish travel horizontally before hitting the water?Concept Check
In a scene in an action movie, a stuntman jumps from the top of one building to the top of another building 4.0 m away. After a running start, he leaps at a velocity of 5.0 m/s at an angle of 15° with respect to the flat roof. Will he make it to the other roof, which is 2.5 m shorter than the building he jumps from?Concept Check
A golfer hits a golf ball at an angle of 25.0° to the ground. If the golf ball covers a horizontal distance of 301.5 m, what is the ball's maximum height? (Hint: At the top of its flight, the ball's vertical velocity component will be zero.)Concept Check
A baseball is thrown at an angle of 25° relative to the ground at a speed of 23.0 m/s. If the ball was caught 42.0 m from the thrower, how long was it in the air? How high did the ball travel before being caught?Concept Check
Salmon often jump waterfalls to reach their breeding grounds. One salmon starts 2.00 m from a waterfall that is 0.55 m tall and jumps at an angle of 32.0°. What must be the salmon's minimum speed to reach the waterfall?Concept Check
Consider a situation in which a car traveling at 90 km/h is passing a car traveling at 80 km/h. What would be the velocity of the faster car with respect to the slower car?Relative Velocity
A plane flies northeast at an airspeed of 563.0 km/h. (Airspeed is the speed of an aircraft relative to the air.) A 48.0 km/h wind is blowing to the southeast. What is the plane's velocity relative to the ground?Concept Check