Suppose this comet were to hit the earth at 40000 km/h and fuse with it. by how much would it change our planet's velocity? (the mass of the earth is 5.97*1024kg)

change in velocity = final velocity - initial velocity = v - u

for comet:

uc = initial velocity of comet (before impact)

vc = final velocity of comet

mc = mass of comet

uc = 40000 kmph

vc = ?

mc = 10 x 10^14 kg

for probe:

up = initial velocity of probe (before impact)

vp = final velocity of probe

mp = mass of probe

up = 37000 kmph

vp = ?

mp = 372 kg

Now,

by principle of conservation of momentum

(mc x uc) - (mp x up) = (mc x vc) + (mp x vp)

Since probe is in comet after collision, vp = vc = V

then,

(mc x uc) - (mp x up) = V (mc + mp)

V = [ (mc x uc) - (mp x up) ] / (mc + mp)

= ((10 * 10^14 * 40000) - (372 * 37000)) : ((10 * 10^14) + 372)

= ?

then,

change in velocity of the comet = ? - (40000) =