Question

In July 2005, NASA's "Deep Impact" mission crashed a 372-kg probe directly onto the surface of the comet Tempel 1, hitting the surface at 37000 km/h relative to the surface. The original speed of the comet at that time was about 40000 km/h, and its mass was estimated to be in the range (0.10−2.5)×1014kg. Use the smallest value of the estimated mass. What change in the comet's velocity did this collision produce? 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

1)

Apply conservation of momentum principles

p1x = p 2x

v 2x = (mA V a1x + mB vB 1x / mA+ mB)

change in velocity = v2x - vB1x = ( mA/ mA+ mB) vA1x + ( mB- mA- mB/ mA+ mB) v B1x

delta v = ( mA/ mA+ mB) ( vA1x- vB1x)

=372/(372+0.10 * 10 ^14 kg) (-37000 km/h)

=-1.4 * 10 ^-6 km/h

the change in comet's velocity is 1.4 * 10 ^-6 km/h

(2) Again same principle

delta v= 0.10 * 10 ^14 kg/ (0.10 * 10 ^14 kg+5.97 * 10 ^24 kg ) (-40000 km/h =-6.7 * 10 ^-8 km/h

the change in planet velocity is 6.7 * 10 ^-8 km/h