If an object is projected vertically upwards with speed, half the escape speed of earth, then the maximum height attained by it is (R is radius of the earth)..?

Applying the law of conservation of energy,Total energy (P.E.+K.E) of the object on the surface of earth=Total energy of the object at a height (h) reached by itSuppose,Mass of earth=MMass of object=mRadius of earth=RThen,-GMmR+12m (vescape2)2=-GMmR+h+12m (0)2But, vescape=2GMRSo, -GMmR+12m (2GMR2)2=-GMmR+hOn solving, we geth=R/3

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