Help with the entire question please! Thanks in advance. (33%) Problem 1: A mete

Question

Help with the entire question please! Thanks in advance.

(33%) Problem 1: A meteoroid is moving towards a planet. It has mass m- 0.78x109 kg and speed v1 -2.9x107 m/s at distance R1 1.6x107 m from the center of the planet. The radius of the planet is R 0.62x10 m. The mass of the planet is M-7.6x1025 kg. There is no air around the planet. Otheexpertta.com 14% Part (a) Enter an expression for the gravitational potential energy El of the meteoroid at R1 in terms of defined quantities and the gravitational constant G. Assume the potential energy is zero at infinity Grade Summarv Deductions Potential PE1- 090 100% Submissions Attempts remaining: 8 % per attempt) detailed view DELCLEAR Submit Hint I give up! Hints:-% deduction per hint. Hints remaining: 2 Feedback: 1% deduction per feedback. 14% Part (b) Calculate the value of PE, in Joules. 1496 Part (c) Enter an expression for the total energy El of the meteoroid at R1 in terms of defined quantities. 14% Part (d) Calculate the value of El, in joules. 14% Part (e) 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 14% Part (f) Enter an expression for V, the meteoroid's speed at the planet's surface. in terms of G. M v1, RI, and R 1496 Part (g) Calculate the value of v in meters per second

Explanation / Answer

a)

gravitational potential energy is given as

PE1= - GMm/R1

b)

inserting the values

PE1= - GMm/R1 = - (6.67 x 10-11) (7.6 x 1025) (0.78 x 109)/(1.6 x 107) = - 2.5 x 10-17 J

c)

E1 = kinetic energy + gravitational potential energy

E1 = (0.5) m V12 - GMm/R1

d)

E1 = (0.5) (0.78 x 109) (2.9 x 107)2 - 2.5 x 10-17

E1 = 3.3. x 1023 J

e)

E = - GMm/R + (0.5) m v2

f)

using conservation of energy

E = E1

- GMm/R + (0.5) m v2 = (0.5) m V12 - GMm/R1

v2 = V12 - 2GM/R1 + 2GM/R

v = sqrt(V12 - 2(GM/R1) + 2(GM/R))

g)

inserting the values

v = sqrt((2.9 x 107)2 - 2((6.67 x 10-11) (7.6 x 1025)/(1.67 x 107)) + 2((6.67 x 10-11) (7.6 x 1025)/(0.62 x 107)))

v = 2.9 x 107 m/s

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