Question

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)

Answer 1

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) =