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The velocity of ball A is V_A = (3*i_hat + 4*j_hat + 5*k_hat) m/s. The speed of ball B is twice the speed of ball A, and ball B moves in the direction of (-i_hat - j_hat). What is the velocity of ball B?

1. 10*i_hat + 10*j_hat
2. -10*i_hat - 10*j_hat
3. 10*i_hat - 10*j_hat
4. -10*i_hat + 10*j_hat

Correct answer: -10*i_hat - 10*j_hat

Solution

|V_A| = 5*sqrt(2), so |V_B| = 10*sqrt(2). Unit vector in direction (-i_hat - j_hat) = (-1/sqrt(2))*i_hat + (-1/sqrt(2))*j_hat. V_B = 10*sqrt(2)*(-1/sqrt(2), -1/sqrt(2), 0) = -10*i_hat - 10*j_hat.

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