g = 1.62 m/s^2 = 0.00162 not 0.0162 km/s^2
but I suspect you have other unit errors
1.453 km/s * 3600 = 5231 km/hr which is awful fast
I get 651 km using your data with the g repaired
A newly established colony on the Moon launches a capsule vertically with an initial speed of 1.453 km/s. Ignoring the rotation of the Moon, what is the maximum height reached by the capsule? km
The answer key is 1040km. I have tried v^2/2g (1.4532km/s)^2/(2*.0162km/s^2) and get the answer as 65.1km but that is not the correct answer. Can somebody shows me how to get to the answer key?
5 answers
our answer isn't even close to the answer key. Have other idea?
have you had calculus?
the launch speed and low moon gravity means that the capsule goes beyond the region where g is relatively constant
the force is related to the height by the universal gravitational equation ... f = G M m / (r + h)^2
force * height = energy ... ∫ de = ∫ f dh = 1/2 m v ^2
sorry, but my calculus is pretty rusty
the launch speed and low moon gravity means that the capsule goes beyond the region where g is relatively constant
the force is related to the height by the universal gravitational equation ... f = G M m / (r + h)^2
force * height = energy ... ∫ de = ∫ f dh = 1/2 m v ^2
sorry, but my calculus is pretty rusty
I think Scott is aiming you in the right direction
F = G M m/r^2
potential energy = integral from infinity to r of F dr
take it at 0 at infinity so it gets negative as you move in
F dr = G M m int dr/r^2 = -G M m /r
so as you move from Ro the surface to R, the increase is
G M m (1/Ro - 1/R)
that = 1/2 m v^2
note that G M/Ro^2 = g
F = G M m/r^2
potential energy = integral from infinity to r of F dr
take it at 0 at infinity so it gets negative as you move in
F dr = G M m int dr/r^2 = -G M m /r
so as you move from Ro the surface to R, the increase is
G M m (1/Ro - 1/R)
that = 1/2 m v^2
note that G M/Ro^2 = g
hey ... this works
the gravitational potential energy of a object at a distance r from a large body is ... G M m / r
the difference in the P.E. on the surface and at altitude is the K.E. at launch
(G M m / r) - [G M m / (r + h)] = 1/2 m v^2
solve for h ... might be easier to plug in numerical values at the beginning
the gravitational potential energy of a object at a distance r from a large body is ... G M m / r
the difference in the P.E. on the surface and at altitude is the K.E. at launch
(G M m / r) - [G M m / (r + h)] = 1/2 m v^2
solve for h ... might be easier to plug in numerical values at the beginning