Physical Applications of Calculus qu. (1 Viewer)

[currysauce]

To do with velocity in terms of x.

If a rockets accl. is given by a = -k/x², where x is the distance form the centre of the Earth, and if the rocket starts from rest at the surface of the Earth (radius 6400km), find an equation for the velocity of the rocket in terms of x.


answer: v = root [ k(6400-x)/3200x ]

 

[shafqat]

To do with velocity in terms of x.

If a rockets accl. is given by a = -k/x², where x is the distance form the centre of the Earth, and if the rocket starts from rest at the surface of the Earth (radius 6400km), find an equation for the velocity of the rocket in terms of x.


answer: v = root [ k(6400-x)/3200x ]

d/dx(v^2/2) = -k/x²
v^2/2 = k/x + c
when x = 6400, v = 0
so c = -k/6400
substitute and solve for v

 

[currysauce]

thankyou good sir