Strings (SiPjAjk) = S7P5A51 Base Sequence = 12735 String Sequence = 12735 - 5 - 51
(a) What initial velocity is needed to send an object to the moon so that it arrives there with zero velocity?
(b) Suppose the moon is not the destination rather the object is to be sent into space so that it never returns. What initial velocity is needed to realize this objective?
(a) S7P5A51 (Physical Change - Velocity).
The Pj Problem of Interest (PPI) is of type change. Problems of speed, velocity, acceleration and time (duration) are change problems.
The initial velocity V, required to send an object up so that it reaches a distance d feet above the surface of the earth is given by:
V2 = 64R(1 - R/(R + d))-----(1). R is the radius of the earth.
(a) d = distance from earth to moon = 240, 000 miles = 240, 000 x 5280 = 1.27 x 109 ft
Radius of earth = 4,000 miles = 4,000 x 5280 = 2.1 x 109 ft
Substituting R and d in equation (1) yields:
V = 36, 500 ft/sec approximately.
So, an object sent up from the surface of the earth requires approximately, 36,500 ft/sec of initial velocity to arrive at the moon. Its velocity will be zero on arrival.
(b) An object sent up from the surface of the earth without the possibility of returning implies its destination is at infinity, that is d = ∞.
When d = ∞, equation (1) becomes:
V2 = 64R -------(2)
So, V = 8√R ----------(3)
In actuality a d = ∞ implies the object has been sent far far away into deep space forever and so the velocity v in equation (3) is called the escape velocity
The point "." is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
Ordinary Differential Equations (ODEs)