(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hint: Disregard any dissipative effects of the

atmosphere of the planet.

A projectile is launched from the surface of a planet (mass M, radius R)

with a launch speed equal to 61 percent of the escape speed for that

planet. The projectile will rise to a maximum height and fall back to the

surface of the planet. What will be the ratio of its maximum height above

the surface to radius of the planet, h/R?

2. Relevant equations

1/2mv² = -Gmm/R

Vf² = Vi² - 2gh

3. The attempt at a solution

1. 1/2mv² = -Gmm/R

v² = -2Gm/R

v = .61√(2Gm/R)

2. Vf² = Vi² - 2gh

0 = Vi² - 2gh

Vi² = 2gh

Vi = √2gh

3. .61√(2Gm/R) = √(2Gh)

.7442(Gm/R) = 2(Gmh/R²)

.7442Gm = 2(Gmh/R)

.7442 = 2h/R

h/R = .3721

Any thoughts or advice on the incorrect answer? Thanks in advance.

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# Homework Help: Find the ratio of maximum height to radius of planet

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