A) write the two conservation of momentum equations in the x and y directions (1

Question

A) write the two conservation of momentum equations in the x and y directions (19 points) Suppose a small asteroid is hurtling toward Earth and the solution is to deflect it with a ball of garbage of equal size and mass. Let the speed of the asteroid be vi 10,000 m/s and the mass of each object be 10kg. The two objects collide at 90 and they stick together to form a single ball object with double the mass, If the asteroid must be deflected by 10°, what is the minimum speed of the ball, va? 3. V1i 10° Earth a. Write the two conservation of momentum equations in the x and y directions.

Explanation / Answer

v1i,x = v1i = 10000 m/s

v1i,y = 0

v2i,x = 0

v2i,y = v2i = ?

m1 = m2 = m

For final:

m = m+m = 2m

vf,x = vf cos10

vf,y = vf sin10

(a)

Along x:

mv1i,x + mv2i,x = 2mvf cos10

=> v1i = 2vf cos10

along y:

mv1i,y + mv2i,y = 2mvf sin10

=> v2i = 2vf sin10

(b)

Solving both eqns:

1 -----> 10,000 = 2vf cos10

=> vf = 5077.13 m/s

2 ------> v2i = 2(5077.13) sin10 = 1763.27 m/s

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