The answer is 10.5 kg m/s
Impulse (I) is the multiplication of force (F) and time interval (Δt): I = F · Δt
Force (F) is the multiplication of mass (m) and acceleration (a): F = m · a
Acceleration (a) can be expressed as change in velocity (v) divided by time interval (Δt): a = Δv/Δt
So:
a = Δv/Δt ⇒ F = m · a = m · Δv/Δt
F = m · Δv/Δt ⇒ I = m · Δv/Δt · Δt
Since Δt can be cancelled out, impulse can be expressed as:
I = m · Δv = m · (v2 - v1)
It is given:
m = 1.5 kg
v1 = 15 m/s
v2 = 22 m/s
I = 1.5 · (22 - 15) = 1.5 · 7 = 10.5 kgm/s.
Answer:
ΔE = GMm/24R
Explanation:
centripetal acceleration a = V^2 / R = 2T/mr
T= kinetic energy
m= mass of satellite, r= radius of earth
= gravitational acceleration = GM / r^2
Now, solving for the kinetic energy:
T = GMm / 2r = -1/2 U,
where U is the potential energy
So the total energy is:
E = T+U = -GMm / 2r
Now we want to find the energy difference as r goes from one orbital radius to another:
ΔE = GMm/2 (1/R_1 - 1/R_2)
So in this case, R_1 is 3R (planet's radius + orbital altitude) and R_2 is 4R
ΔE = GMm/2R (1/3 - 1/4)
ΔE = GMm/24R
