Question

A body is projected vertically upward from the surface of the earth with a velocity equal to half the escape velocity. If r is the radius of the earth, then the maximum height attained by the body is

Answer 1

We know, that Escape Velocity of the earth is given by the Formula,

Ve = √(2gr)

Since, Speed of the object is half the escape velocity.

Therefore,

    $u = \sqrt{\frac{gr}{2} }$

Now, Final speed(v) = 0

Initial speed (u) = $u = \sqrt{\frac{gr}{2} }$

Applying third equation of motion,

v² - u² = 2gh

(0)² -(√(gr/2))² = 2(-g)h          

[Since, It is moving upward, hence acceleration = -g.]

gr/2 = 2gh

h = r/4

Hope it helps.