A particle of mass m is projected from the surface of the earth with velocity $$10$$ $$km/$$$$sec$$ at an angle $$60o$$ 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$$.

Question

Infinity Learn · Accepted Answer

Conservation of momentum at P and $$Qmv0cos$$⁡θ$$R=m$$ v (R$$ $$+h) $$v=RR+hv0cos$$⁡θ v

Motion of planets and satellites

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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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Motion of planets and satellites

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Conservation of momentum at P and Qmv0cos⁡θR=m v (R +h) v=RR+hv0cos⁡θ v<v0cos⁡θ or v<(10)12or v<5km/sec

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