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alayciaruffin076
05.12.2020 •
Physics
) A striker can give the ball an initial speed of 30m/s. Within what two elevation angles must he kick
the ball to score a goal from a point 50m in front of the goalposts whose horizontal bar is 2.44m
above the ground?
(
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Ответ:
about 19.6° and 73.2°
Explanation:
The equation for ballistic motion in Cartesian coordinates for some launch angle α can be written ...
y = -4.9(x/s·sec(α))² +x·tan(α)
where s is the launch speed in meters per second.
We want y=2.44 for x=50, so this resolves to a quadratic equation in tan(α):
-13.6111·tan(α)² +50·tan(α) -16.0511 = 0
This has solutions ...
tan(α) = 0.355408 or 3.31806
The corresponding angles are ...
α = 19.5656° or 73.2282°
The elevation angle must lie between 19.6° and 73.2° for the ball to score a goal.
_____
I find it convenient to use a graphing calculator to find solutions for problems of this sort. In the attachment, we have used x as the angle in degrees, and written the function so that x-intercepts are the solutions.
Ответ:
The angular displacement of the wheel is 554.5 rad
Explanation: Please see the attachments below