A small asteroid (mass of 52 g.)strikes a glancing blow at a satellite in empty

Question

A small asteroid (mass of 52 g.)strikes a glancing blow at a satellite in empty space. The satellite was initially at rest and the asteroid was traveling at 2100 m/s. The satellite's mass is 110 kg. The asteroid is deflected 10 degree from its original direction and its speed decreases to 1100 m/s. but neither object loses mass. Part A Determine the direction and of the satellite after the collision. Assume the initial direction of the asteroid as 4-x-axis. Part B Determine the speed of the satellite after the collision.

Explanation / Answer

Let us assume that the original direction of the asteroid is along the x-axis, and is deflected 100 above the x-axis.

Let '' be the angle below the x-axis at which the satellite is deflected after collision and 'v' be its velocity

Conserving momentum along the x-axis,

(52*10-3)(2100) = (52*10-3)(1100)(cos100) + (110)(v)(cos)

=> 165.53 = (110)(v)(cos)

=> cos = 0.48063/v    ......................(1)

Conserving momentum along the y-axis,

0 = (52*10-3)(1100)(sin100) - (110)(v)(sin)

=> sin = 0.09029/v   ........................(2)

Dividing (2) by (1), we get

Tan = 0.18786

=> = 10.63944

=> = 10.64

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