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A projectile of mas s m is fired from the surface of earth at an angle α=60∘ from the vertical. The initial speed m of the projectile is u=GMR, where M and R are mass and radius of the earth. Find the height by the projectile in kilometer. Neglect air resistance and the rotation of earth. (Given R = 6400 km)

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Detailed Solution

Let v be the speed of projectile at the highest point. By conservation of angular momentum and conservation of mechanical energy, we havemuRsin⁡α=mvrmax and 12mu2−GMmR=12mv2−GMmrmaxSolving these two equations, we get rmax=3R2∴ hmax=rmax −R=R2=3200km

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A projectile of mas s m is fired from the surface of earth at an angle α=60∘ from the vertical. The initial speed m of the projectile is u=GMR, where M and R are mass and radius of the earth. Find the height by the projectile in kilometer. Neglect air resistance and the rotation of earth. (Given R = 6400 km)