Q.

A projectile of mass m is fired from the surface of earth at an angle α=60∘ from the vertical. The initial speed 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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answer is 3200.

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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−GMmrmax Solving these two equations, we get rmax=3R2∴ hmax=rmax−R=R2=3200km
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A projectile of mass m is fired from the surface of earth at an angle α=60∘ from the vertical. The initial speed 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)