Question:
(a) What change in the comet’s velocity did this collision produce? Would this change be noticeable? (b) Suppose this comet were to hit the earth and fuse with it. By how much would it change our planet’s velocity? Would this change be noticeable? (The mass of the earth is 5.97×1024kg.)
Answer:
The answers to the question are;
(a) The change in the comet’s velocity produced by the collision is 2.86 × 10⁻⁶km/h or 7.944 × 10⁻⁷ m/s
(b) It would change our planet’s velocity by 6.70× 10⁻⁸ km/h or 1.86× 10⁻⁸ m/s
Change is too small to be noticeable
Explanation:
We not that the question is about conservation of liner momentum
Therefore we have, by listing out the known parameters
m₁ = Mass of "Deep Impact" = 372 kg
m₂ = Mass of Tempel 1 comet = (0.1 to 2.5) × 10¹⁴ kg,
v₁ = Vaelocity of "Deep Impact" = 37000 km/h
v₂ = Velocity of Tempel 1 comet = 40000 km/h
From the principle of linear momentum, we have, for both bodies moving in opposite direction;
m₁×v₁ + m₂×v₂ = m₁×v₃ + m₂×v₃ since it was a crash, it is assumed that they both have the same final velocity
This gives
372 kg ×37000 km/h - 0.1 × 10¹⁴ kg × 40000 km/h = (372 kg + 0.1 × 10¹⁴ kg )×v₃
13764000 kg·km/h - 4.0 × 10¹⁷ kg·km/h = 10000000000372×v₃
v₃ = (-399999999986236000 kg·km/h)/10000000000372 = -39999.999997 km/h ≈ - 40000 km/h in the direction of Deep Impact
Change in comet velocity
= 40000 km/h - 39999.999997 km/h
= 2.86 × 10⁻⁶km/h = 7.944 × 10⁻⁷ m/s
(b) If the colission is with earth, we have
m₃ = Mass of earth
From the principle of conservation of linear momentum, we have
m₂v₂+m₃ v₃ = (m₂ + m₃) v₄
v₃ = Initial velocity of Earth = 0 km/h
m₃ = Mass of Earth = 5.97 × 10²⁴ kg
Therefore, pluggin in the vaalues gives
0.1 × 10¹⁴ kg × 40000 km/h + 5.97 × 10²⁴ kg × 0 km/h = (0.1 × 10¹⁴ kg + 5.97 × 10²⁴ kg) × v₄
Therefore,
v₄ = (4.0 × 10¹⁷ kg·km/h + 0 kg·km/h)/ (5970000000010000000000000 kg)
= 6.70× 10⁻⁸ km/h = 1.86× 10⁻⁸ m/s
Change is too small
= Gravitational force
= mass of 1st body
= mass of 2nd body