Question

As part of an interview for a summer job with the Coast Guard, you have been asked to help determine the search area for two sunken ships by calculating their velocity just after an accident. According to the last radio transmission from the luxury liner Apollo (3.9 × 104 metric tons), it was going due east at a steady speed of 21 knots in calm seas through a rare fog just before it was struck broadside by the freighter Blake (6.1 × 104 metric tons), which was traveling north at steady speed of 11 knots. The transmission also noted that when the freighter's bow pierced the hull of the liner, the two ships stuck together and sank. What was the speed and direction of the ships after the collision ? (Take zero degrees to be straight east and counter-clockwise as positive.)

1)____ knots

2)____ degrees

Answer 1

Answer :

step:1

given that

mass m1=3.9*10^4 metric tons

mass m2=6.1*10^4 metric tons

Conservation 1Knot = 0.51444 m/s

speed u1=21 knots =10.803324 m/s

speed u2=11 knots = 5.658884 m/s

step:2

both are moving perpendicular to each other

if they collided , stick together and move with a common speed of V

m1u1+m2u2 = (m1+m2)u

   V = m1u1+m2u2 / (m1+m2)
   = (3.9*10^4 *10.803324+6.1*10^4 * 5.658884) / (3.9*10^4+6.1*10^4 ) m/s
   =766521.56 / 1*10^5

= 7.6652 m/s

now the direction is Tan theta (u2/u1) ==> theta = arc tan (u2/u2)

because m2 moving towards north and m1 movign east so m1 haveonly x- component and m2 having on;y y- component , both will move in 1st quadrant then tan theta = vy/vx

               theta=arc tan (5.658884/10.03324)

               theta =29.42degrees

the direction is in the first quadrant , 29.42 degrees with x axis moves with7.6652 m/s