Homework Statement
Given |\vec{a}| = 8, |\vec{b}| = 9 and the angle between vector \vec{a} and \vec{b} is 48° find the cross product, \vec{a} X \vec{b}.
Homework Equations
Let θ = angle between \vec{a} and \vec{b}.
\vec{a} . \vec{b} = ( \vec{x}1 * \vec{x}2 ) + ( \vec{y}1 * \vec{y}2 ) + (...
The Question
The Planet V has a year lasting 360 days. In the same star system is the Planet X. The Planet X has half the mass and triple the radius. A planet X year would be approximately _____ days
The attempt at a solution
Givens:
Tv= 360days
Tx= ?
mv = mv
mx = 1/2mv
rv = rv
rx = 3rvI...
Forgot that Fg = -GMm / r^2 so that the - cancel out:
F = ma
a = F / m
a = ( -Fg + Fe + Fb ) / m
a = [-(-GMm/r^2) + (KQq/r^2) + (qvBsin90)]/m
a = [-(-(6.67*10^-11)(5*10^25 kg)(10000 kg)/(20000000 m)^2) + ((9.0*10^9)(+10^6 C)(+5 C)/(20000000 m)^2) + ((+5 C)(10000 m/s)(0.001 T)(1))/(10000 kg)]
a...
mPerturbation = 10 tonnes = 10000 kg
mConniption = 5 * 10^25 kg
charge of Conniption [Q] = +10^6 C
charge of Perturbation [q] = +5 C
rConniption = 10500000 m
altitude Perturbation = 9500000 m
r = rCon + altitPert = 20000000
v Perturbation = 10000 m/s
B Conniption = 0.001 T (perpendicular...
The forces that are involved in this question from what I can tell are gravitational and magnetic.
Some possible relevant formulas are:
Fg = GMm / r^2
Fe = kQq / r^2
Fb = qvBSin(theta)
I think it would be required to substitute these into F = ma to solve for 'a' somehow, but I am not sure.
Find new velocity:
K = mv^2 / 2
(9.973 * 10^9)+(9.97165 * 10^10) = (1000)v^2 / 2
v = √(2)(1.096895*10^11)/1000
v = 14811.44827 = 1.481 * 10^4 m/s
This is the actual velocity so therefore the rocket will have sufficient velocity to escape.
Find orbital velocity:
v = √(GM/r)
v = √((6.67*10^-11)(5.98*10^24)/(13620000 + 6380000)
v = 4.466 * 10^3 m/s
Find orbital kinetic energy:
K = mv^2/2
k = (1000)(4.466*10^3)^2/2
K = 9972578000 = 9.973 * 10^9 J
Find escape velocity:
v esc = √2 v
v esc = √2 (4.466 * 10^3)
v esc =...
1. The meteoroid Perturbation passes near the planet Conniption which has a mass of 5 * 10^25kg, a charge of +10^6 C and has a radius of 10500km. The meteoroid has a mass of 10 tonnes and a charge of +5 C. The meteoriod has an altitude of 9500km and a velocity of 10km/s. The planets magnetic...
[b]1.Nasa fires a 1 tonne space probe, from a stable orbit of altitude 13,620km using a giant rail gun. The rail gun provides the probe with 9.97165*10^10 J of additional kinetic energy. Determine if the probe has enough velocity to escape the Earth's gravity well. The Earth's mass and radius...