A planet of mass M and radius R has no atmosphere. The escape velocity at its surface is ve. An object of mass m is at rest a distance r from the center of the planet, where r>>R. The particle falls to the surface of the planet. The total mechanical energy of the particle at the surface of the planet is closest to

Explanation:

Expression for escape velocity

ve =

ve² R / 2 = GM

M is mass of the planet , R is radius of the planet .

At distance r >> R , potential energy of object

=

Since the object is at rest at that point , kinetic energy  will be zero .

Total mechanical energy  = + 0 =

Putting the value of GM = ve² R / 2

Total mechanical energy  = ve² Rm / 2 r

This mechanical energy will be conserved while falling down on the earth due to law of conservation of mechanical energy  . So at surface of the earth , total mechanical energy

=  ve² Rm / 2 r

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle