A balloon starts rising from the surface of the earth with vertical component of velocity `v_(0)`. The balloon gathers a horizontal velocity `v_(x) = ay`, where a is a constant and y is the height from the surface of the earth, due to a horizontal wind. Determine
(a) the equation of trajectory of the balloon.
(b) the tangential, normal and total acceleration of the balloon as function of y.

A balloon starts rising from the surface of the earth with a verticle component of velocity v_(0) . The baloon gathes a horizontal velocity v_(x)=lambda_(y) , where lambda is a constant and y is the height from the surface of earth, due to a horizontaln wind. determine (a) the equation of trajectory and (b) the tangential, normal and total acceleration of the balloon as a function of y .

A balloon starts rising from the surface of the Earth. The ascertion rate is constant and equal to v_0 . Due to the wind the balloon

A balloon starts rising from the earth's surface. The ascension rate is constant and equal to v_(0) . Due to the wind. The balloon gathers the horizontal velocity component v_(x)=ky , where k is a constnat and y is the height of ascent. Find how the following quantities depednd on the height of ascent. (a) the horizontal drift of the balloon x (y) (b) the total tangential and normal accelrations of the balloon.

A body is imparted a velocity v from the surface of the earth. If v_(0) is orbital velocity and v_(e) be the escape velocity then for :

A balloon of mass m is rising up with an acceleration a.

A body is projected vertically upward from the surface of the earth with escape velocity. Calculate the time in which it will be at a height (measured from the surface of the arth) 8 time the radius of the earth (R). Acceleration due to gravity on the surface of the earth is g.

The escape velocity of a body from the surface of the earth is V_(1) and from an altitude equal to twice the radius of the earth, is, V_(2) . Then

If V, R and g denote respectively the escape velocity from the surface of the earth radius of the earth, and acceleration due to gravity, then the correct equation is