First slide

Motion of planets and satellites

Question

A particle of mass m is projected from the surface of the earth with velocity 10 km/sec at an angle 60^o with horizontal. If V is the speed of the particle at the point of maximum height of the particle from the surface of the earth, then find the value of V which will be less than (a minimum value of velocity in km/sec) an integer from 0 to 9.

Moderate

Solution

Conservation of momentum at P and Q $({mv}_{0} \cos θ) R =$ m v (R +h)
$v = (\frac{R}{R + h}) v_{0} \cos θ v < v_{0} \cos θ$
$\begin{array}{l} or v < (10) (\frac{1}{2}) \\ or v < 5 km / \sec \end{array}$

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