Water in a river flows with a component downstream (x-direction) of 6 m/s and a component across the stream (y-direction) of 4 m/s. A boat is attempting to cross the river. The velocity of the boat relative to the water is 20 m/s at an angle of 70 degrees with respect to the x-axis. Determine the velocity of the boat relative to the shore.

A cannon ball is fired with an initial speed of 123 m/s at an angle of 60 degrees from the horizontal.Express the initial velocity as a linear combination of its unit vector components.Find the maximum height reached by the cannon ball and the time needed to reach the maximum height.Find the speed of the cannon ball at the maximum height and the magnitude of its acceleration.

A dolphin wants to swim directly back to its home bay, which is 0.800 km due west. It can swim at a speed of 5.00 m/s relative to the water, but a uniform water current flows with speed 2.83 m/s in the southeast direction. What direction should the dolphin head? Enter the angle in degrees where positive indicates south of west and negative indicates north of west.

A plane is headed due west with an air speed of 207 m/s. The wind blows south at 20.0 m/s. Find the velocity of the plane relative to the earth.To solve this problem it will be necessary to determine the plane's velocity relative to the the air. What is the plane's east-west velocity relative to the air? (Define the positive direction to be east.)Additionally, to solve this problem it will be necessary to determine the air's velocity relative to the earth. What is the air's north-south velocity relative to the earth? (Define the positive direction to be north.)

You are climbing the stairs to the second floor with a speed of 3 m/s while a raindrop is sliding down the back of your coat at a speed of 0.3 m/s. The stairs make an angle of 40 degrees with the horizontal. We are interested in the velocity of the raindrop relative to the ground? The problem has three velocitiesvector(pg) = velocity of you relative to the ground vector(dp) = velocity of drop relative to youvector(dg) = velocity of drop relative to the ground 1. Draw vectors for the two given velocities into the coordinate system. Please show the angle theta = 40 degrees. 2. Collect the information about the speeds and calculate the x- and y-components of the given velocities. 3. Express vector(dg) in terms of the other velocities; then write the equations for the x-and the y-component of vector(dg) (no numbers). 4. Calculate the x- and y-components of the velocity of the drop relative to the ground. 5. Check your calculations with a graphical addition of velocity vectors in the…

A plane releases a package from an altitude of 300 meters. At the time of release, both the plane and package are moving at 100 meters per second, directed at an angle of 20 degrees below the horizontal. How long is the package in the air? Find the magnitude and direction of the velocity of the package just before impact? Draw a sketch or diagram of the problem. Thank you for your help.

A glider aircraft initially traveling due west at 86.0 km/h encounters a sudden gust of wind at 40.0 km/h directed toward the northeast (see the figure below). What are the speed and direction of the glider relative to the ground during the wind gust? (The velocity of the glider with respect to the ground is the velocity of the gilder with respect to the wind plus the velocity of the wind with respect to the ground.)

Chinook salmon are able to move upstream faster by jumping out of the water periodically; this behavior is called porpoising. Suppose a salmon swimming in still water jumps out of the water with a speed of 6.26 m/s at an angle of 30°, sails through the air a distance L before returning to the water, and then swims a distance L under water at a speed of 3.70 m/s before beginning another porpoising maneuver. Determine the average speed of the fish.

A boat that can travel at 2.50 m/s in still water is heading directly across a river that is flowing at a rate of 1.25 m/s, i.e., so that it will end up downstream. (a) What is the velocity of the boat as measured by a person standing on the shore? Give both the magnitude and the angle. (b) If the river is 175 m across, how long does it take the boat to cross the river and in this time how far down stream will the boat have traveled? (c) Provide a diagram of the situation.

For this problem, you can think of the jet stream as a river of air. Across the United States, the jet stream usually moves from west to east. We will assume that the jet stream is moving in its usual direction at 9.00 x 101 km/hr. On a particular day, you need to pilot a plane from one city to another that is 4.50 x 102 km directly to the south. The top speed of the aircraft in still air is 285 km/hr. (a) Make a sketch to represent what is happening in this problem. Label all quantities that you know. (b) Using cardinal directions (north, east, south, west) to give a heading, which direction should you aim the plane to reach the city directly to the south at top speed? (c) How fast (in km/hr) would you be moving relative to the ground? (c) How much time (in hr) will it take you to reach your destination?