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seraphim [82]
3 years ago
6

The velocity at the midway point of a ball able to reach a height y when thrown with velocity vi at the origin is:

Physics
1 answer:
Nutka1998 [239]3 years ago
7 0
Assuming the ball follows classical 2D projectile motion (moves in a parabola) and that the height y = the maximum height the ball goes in the y direction (because this would be its midpoint), then the velocity at height y is equal to the initial x component of velocity. At the midpoint, the y component is zero, so the velocity only depends on the x component. Projectiles move at constant speed in the x direction, so X = Xo. As long as you know actual values for Vi and either the initial angle or one initial component, then you can solve for Xo using trigonometry. Xo is thus the velocity of the ball once it has reached its maximum height. 
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Answer:

2.66x10^33 J

Explanation:

In order to do this, we first need to know the expression for kinetic energy:

E = 1/2 I*w²  (1)

I is moment of innertia

w is angular speed.

Moment of Innertia can be calculated using the following expression:

I = 2/5 M*R²  (2)

M is mass of earth, R is radius of earth

Replacing the data in expression (2) we have:

I = 2/5 * 5.97x10^24 * (6.37x10^6)²

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Next, we need to calculate the angular speed of Earth over it's axis, this is easy, because we know the Earth rotates over it's own axis once a day, 24 hours (86400 s), and assuming Earth is a perfect sphere, we can calculate the speed:

w = 2π / 86400 = 7.27x10^-5 rad/s

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E = 2.56x10^29 J

Now that we have this value, we can finally calculate the rotational kinetic energy of earth about the sun. For that, we need to calculate again the angular speed of earth about the sun. The Earth rotates around the sun once a year, or 365 days, which is 3.1536x10^7 s, so the angular speed would be:

w = 2π/3.1536x10^7 = 1.99x10^-7 rad/s

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K = 1/2 (Ie + Me*Rorb²)wo²

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Me mass of earth

Rorb RAdius of orbit around the sun

wo is angular speed around the sun

Replacing the data we finally have:

K = 1/2 [9.69x10^37 + 5.97x10^24 * (1.5x10^11)²]*(1.99x10^-7)²

K = 2.66x10^33 J

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