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nlexa [21]
3 years ago
13

As part of an interview for a summer job with the Coast Guard, you are asked to help determine the search area for two sunken sh

ips by calculating their velocity just after they collided. According to the last radio transmission from the 40,000-ton luxury liner, the Hedonist, it was going due west at a speed of 20 knots in calm seas through a rare fog just before it was struck broadside by the 60,000- ton freighter, the Ironhorse, which was traveling north at 10 knots. The transmission also noted that when the freighter's bow pierced the hull of the liner, the two ships stuck together and sank together. To determine the search area find the resulting components of the velocity.
Physics
1 answer:
marshall27 [118]3 years ago
8 0

Answer:

The resultant velocity is  v_t=10 knots

Explanation:

Apply the law of conservation of momentum

     M_L *v_L + M_f * V_f = (M_L + M_f) v_t

Where M_L is the mass of the Luxury Liner = 40,000 ton

            v_L is the velocity of Luxury Liner = 20 knots due west

            M_f mass of freighter = 60,000

           v_f is the velocity of freighter = 10 knots due north

Apply the law of conservation of momentum toward the the west direction

         v_f = 0 \ knots

So the equation would be

              M_L *v_L = (M_L + M_f) v_t

Substituting values

            40000*20 = (40000+ 60000)v_t_w

Where v_t_w the final velocity due west

Making v_t_w the subject

          v_t_w = \frac{40,000* 20}{(40000 + 60000)}

                = 8 \ knots

Apply the law of conservation of momentum toward the the north direction          

          v_L = 0 \ knots

So the equation would be

           M_f *v_f = (M_L + M_f) v_t_n

Where v_t_n the final velocity due north

     Making v_t_n the subject

          v_t_n = \frac{60,000* 10}{(40000 + 60000)}

                = 6 \ knots

The resultant velocity is

       v_t = \sqrt{v_t_w^2 + v_t_n^2}

            = \sqrt{8^2 +6^2}

           v_t=10 knots

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