A meteoroid is moving towards a planet. It has mass m = 0.18×109 kg and speed v1 = 3.8×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.26×107 m. The mass of the planet is M = 10×1025 kg. There is no air around the planet.a)Enter an expression for the total energy E1 of the meteoroid at R1 in terms of defined quantities. b)Calculate the value of E1, in joules. c)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. m dv,R

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Author:Paul W. Zitzewitz

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Question

A meteoroid is moving towards a planet. It has mass m = 0.18×10⁹ kg and speed v₁ = 3.8×10⁷ m/s at distance R₁ = 1.6×10⁷ m from the center of the planet. The radius of the planet is R = 0.26×10⁷ m. The mass of the planet is M = 10×10²⁵ kg. There is no air around the planet.

a)Enter an expression for the total energy E₁ of the meteoroid at R₁ in terms of defined quantities.

b)Calculate the value of E₁, in joules.

c)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface.

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Step 1: Determine the given variables:

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Step 2: (a) Expression of total energy E1 of the meteoroid at R1 in terms of defined quantities:

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Step 3: b)Calculate the value of E1, in joules:

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Step 4: (c) Enter an expression for the total energy E of the meteoroid at R and speed v:

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