A yacht is pushed along at a constant velocity by the wind. The wind force is 180N at an angle of 25 degrees to the direction of
the of the motion of the yacht. By resolving the wind force parallel and perpendicular to the direction of motion, determine the component of the wind force in the direction of motion.
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Answer:
2560m or 2.56km (rounded to 3 significant figures)
Explanation:
First, list all known and desired values/variables (initial vertical velocity is 0 as the plane is kept level and vertical acceleration is just gravity):
The horizontal displacement is going to be the distance travelled, horizontally of course, once the package is released;
First thing to understand is that the vertical and horizontal components are to be dealt with separately because they don't affect each other;
Since there is no horizontal acceleration (ignoring air resistance), we simply require a velocity and time to find the horizontal displacement, using the formula v = d/t (or speed = distance/time);
What we have is the horizontal velocity but we don't have the time taken;
One thing we know is that the time elapsed for the vertical fall of 800m and for the horizontal displacement must be the same;
What we do, therefore, is find the time taken for the vertical displacement using the formula, s = ut + ¹/₂·at², since we know the vertical velocity, height and acceleration:
800 = (0)t + ¹/₂·(9.8)t²
800 = 4.9t²
t² = 163.26...
t = 12.77...
We now have the time taken for the vertical fall and the horizontal displacement, we can use this with the horizontal velocity we know already and get the horizontal displacement: