(7 points) Dynamics/Collisions In June of 2005 the NASA spacecraft Deep Impact l

Question

(7 points) Dynamics/Collisions In June of 2005 the NASA spacecraft Deep Impact launched a 370 kg projectile (called an impactor) into the surface of the comet Tempel 1 The longest dimension of the impactor was about 2 meters. The impactor struck the comet with a speed (with respect to the center of mass of the comet) of 10.30 km/s, embedding itself in the comet. The collision excavated a crater 42 meters deep. The comet is a roughly spherical body with a diameter of about 5 km. The mass of Tempel 1 at time of impact was approximately 7.9x10 kg. Compute the maximum possible change in translational speed of Tempel 1 due to the collision Bonus (3 points) Compute the average force exerted on the impactor by the comet during the collision

Explanation / Answer

The collision between the impactor and the comet is purely inelastic.

So, the momentum of the system before and after the collision will be conserved

mu = [M+m]V

370(10.3 x 103) = [370 + 7.9 x 1013]V

=> V = 4.824 x 10-8 m/s

this is the maximum possible change in speed of the comet after the collision.

now distance traveled by the impactor inside the comet is:

d = 42 m

use v2 = u2 + 2ad

=> 0 = [10.3 x 102]2 + 2a(42)

=> a = - 1.263 x 106 m/s2

therefore, the average force on the impactor will be:

|F| = ma = 370 x 1.263 x 106 = 4.673 x 108 N.

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