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A 67 kg man stands at the front end of a uniform boat of mass 179 kg and of length, L = 2.5 m. Assume there is no friction or drag between the boat and water.
(a) What is the location of the center of mass of the system when the origin of our coordinate system (i) on the man's original location (ii) on the back end of the boat? [4 marks]
(b) If the man walks from the front end to the back end of the boat, by how much is the boat displaced? [3 marks]
(c) Now consider the man and his friend with identical mass of 67 kg are rowing the boat on a hot summer afternoon when they decide to go for a swim. The man jumps off the front of the boat at speed 3 m/s and his friend jumps off the back at speed 4 m/s. If the boat was moving forward at 1.5 m/s when they jumped, what is the speed of the boat after their jump?

Respuesta :

Answer:

Explanation:

ai. com=(67*0+179*1.25)/(179+67)=0.91m

ii. com=(67*2.5+179*1.25)/(179+67)=1.59m

b. 0.91=(67(2.5-d)+179(1.25-d))/(179+67)

   d=0.68m

c. 1.5=(67*-3+67*-4+179*v)/(67+67+179)

    v=5.24m/s

batolisis

The answers to your question are ;

A) Location of the center of the mass of system when origin of coordinate system is

i) On the original location of man = 0.91 m

ii) On back end of boat = 1.59 m

B) The boat is displaced by = 0.68 m

C) speed of boat after their jump ( V ) = 5.24 m/s

Given data :

mass of man = 67 kg

mass of boat = 179 kg

length of boat = 2.5 m

assumptions : No friction/drag force

Solutions

A) determine location of center of mass

i) On the man's original location = 0

= ( mass of man * 0 + mass * 1.25 ) / ( mass of boat + mass of man)

=  ( 0 + 179 * 1.25 ) /  ( 179 + 67 )

= ( 0 + 223.75 ) / ( 246 ) = 0.9096  ≈ 0.91 m

ii) On the back end of the boat

= ( mass of man * length of boat + mass of boat * 1.25 ) / ( mass of boat + mass of man )

= (  67 * 2.5 + 179 * 1.25 ) / ( 179 + 67 )

= ( 167.5 + 223.75 ) / ( 246 ) = 1.590 m

B) By How much is the boat displaced ( d )

0.91 ( location of center of mass from man's original location )

0.91  = (  67 *  (2.5 - d) +  179 (  1.25 - d ) ) / ( 179 + 67 )

        = ( 67 * ( 2.5 - d ) + 223.75 - 179d )) / ( 246 )

∴ d ≈ 0.68 m

C) Determine speed of boat after the jump

Initial speed of boat = 1.5 m/s

hence speed after the jump ( v )

speed of first man = 3 m/s

speed of second man = 4 m/s

1.5 m/s = ( 67 * -3 + 67 * -4 + 179 * v ) / ( 67 + 67 + 179 )

           = ( - 201 + -268 + 179v ) / ( 313 )

∴ v ≈ 5.24 m/s

learn more at : https://brainly.com/question/21759698

 

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