Can I have some help
1 answer:
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Answer:
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.
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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.
(a)
<u>Explanation:</u>
Given:
Moment of Inertia of m₁ about the axis, I₁ = m₁x²
Moment of Inertia of m₂ about the axis. I₂ = m₂ (L - x)²
Kinetic energy is rotational.
Total kinetic energy is
Work done is change in kinetic energy.
To minimize E, differentiate wrt x and equate to zero.
Alternatively, work done is minimum when the axis passes through the center of mass.
Center of mass is at