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) =