The velocity of the wind relative to the water is crucial to sailboats. Suppose a sailboat is in an ocean current that has a velocity of m/s in a direction east of north relative to the Earth. It encounters a wind that has a velocity of m/s in a direction of south of west relative to the Earth. What is the velocity of the wind relative to the water?
The velocity of the wind relative to that of water is 68 m/s. The resultant vector has the direction of SW .
Velocity is the rate of change in position of an item in motion as seen from a specific frame of reference and measured by a specific time standard.
On the ship, you will see that the body is in the y-direction only. The details are given in the sketch. W represents the water, a represents the wind.
Hence the velocity can be calculated by the following equation.
The velocity of the sandal relative to the ship is -17.1 m/s
The component table will be as below:
Here we need to find the x component and the y component.
Hence, the velocity of water w.r.t earth:
Hence the resultant vector will be
Hence the velocity of the wind relative to that of water is 6.68 m/s.
The direction of the velocity will be;
The resultant vector has the direction of .
An owl is carrying a mouse to the chicks in its nest. Its position at that
time is 4.00 m west and 12.0 m above the center of the 30.0 cm diameter nest. The owl is flying east at 3.50 m/s at an angle 30.0º below the horizontal when it accidentally drops the mouse. Is the owl lucky enough to have the mouse hit the nest? To answer this question, calculate the horizontal position of the mouse when it has fallen 12.0 m.
Construct Your Own Problem Consider an airplane headed for a runway in a cross wind. Construct a problem in which you calculate the angle the airplane must fly relative to the air mass in order to have a velocity parallel to the runway. Among the things to consider are the direction of the runway, the wind speed and direction (its velocity) and the speed of the plane relative to the air mass. Also calculate the speed of the airplane relative to the ground. Discuss any last minute maneuvers the pilot might have to perform in order for the plane to land with its wheels pointing straight down the runway.
Solve the following problem using analytical techniques: Suppose you walk straight west and then straight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements and , as in Figure, then this problem asks you to find their sum .)
The two displacements and add to give a total displacement having magnitude and direction .
Note that you can also solve this graphically. Discuss why the analytical technique for solving this problem is potentially more accurate than the graphical technique.
A football quarterback is moving straight backward at a speed of m/s when he throws a pass to a player m straight downfield. The ball is thrown at an angle of role="math" localid="1668669019911" relative to the ground and is caught at the same height as it is released. What is the initial velocity of the ball relative to the quarterback?
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