Physics

Part A:

1. A homing pigeon flies 25 m/s when there is no wind. On the day of the worldwide homing pigeon races, you get a favorable tail wind of 7 m/s. How fast does your homing pigeon fly?

2. On the way home, your pigeon must fly against the 7 m/s wind. How fast does the pigeon fly on the way home?

3. You are boating up a river. Your boat provides enough power to go 15 m/s on still water but the river has a current of 11 m/s in the opposite direction. How fast are you going in relation to the land?
4. An airplane takes off going 85 km/hour at an angle of 35 degrees above the horizon. Break this vector into x and y components.

5. Add the following vectors and find the resultant vector—both magnitude and direction. Vector 1: 23 Newtons @ 17 degrees and Vector 2: 57 Newtons @ 9 degrees.

Step1: Sketch each of the vectors and label with speed and direction.

Step 2: Find the 0-components of each vector and add them together. Step 3: Find the y-component of each vector and add them together. Step 4: Use the new x and y components to create a new right angled triangle in which the hypotenuse is the Resultant vector.

Step : Use the pythagorean theorem to find the magnitude of the resultant vector. Step 6: Use SOH-CAH-TOA to find the angle of the resultant vector. Step 7: Write your final answer in one complete statement that inlcudes both magnitude and direction.

 

Part B:

Real World Problems (15 points each) The map below shows the flight path for someone traveling from Washington DC and passing above Indianapolis, Indiana; Lincoln, Nebraska (hometown of the University of Nebraska High School!) and landing in San Francisco. For the sake of clarity, we will assume that the plane is flying due West the entire trip. The plane’s engines put out enough power to fly at 545 mph if there is no wind (but they could put out more if needed).

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1. Show all your work including both a diagram and algebraic solution. When the plane crosses over Indianapolis, the wind speed at flight altitude is 45 mph @ 45 degrees South of East. If the plane does not make any corrective action, the wind will both slow it down and knock it off course. Calculate the new velocity vector (both magnitude and direction) for the plane?

2. Show all your work including both a diagram and algebraic solution. When crossing over Lincoln, Nebraska, the plane runs into a headwind of 25 mph due East. If the plane does not make any corrective action, it will slow down and arrive in San Francisco late. How fast would the plane have to fly in order to maintain its intended speed and not lose any time?

3. Show all your work including both a diagram and algebraic solution. When the plane crosses the border to Utah, it encounters a cross wind of 15 mph 5 degrees West of North. What speed and direction must the plane head in to keep going due West at 545 mph?

 

Part C:

1. Write your own problem that requires you to add vectors that are parallel to each other and going in the same direction. Solve the problem and include both the algebraic solution and a diagram for your solution.

2. Write your own vector problem that requires you to add vectors that are parallel to each other but going in opposite directions. Solve the problem and include both the algebraic solution and a diagram for your solution.

3. Write your own vector problem that requires you to break at least two vectors into components, add them together and find the resultant vector. Solve the problem and include both the algebraic solution and a diagram for your solution.