contestada

A boat is moving in a river with a current that has speed vW with respect to the shore. The boat first moves downstream (i.e. in the direction of the current) at a constant speed, vB , with respect to the water. The boat travels a distance D in a time tOut . The boat then changes direction to move upstream (i.e. against the direction of the current) at a constant speed, vB , with respect to the water, and returns to its original starting point (located a distance D from the turn-around point) in a time tIn .
1) What is tOut in terms of vW, vB, and D, as needed?
2) What is tIn in terms of vW, vB, and D, as needed?
3) Assuming D = 120 m, tIn = 170 s, and vW = 0.3 m/s, what is vB, the speed of the boat with respect to the water?
4) Once again, assuming D = 120 m, tIn = 170 s, and vW = 0.3 m/s, what is tOut, the time it takes the boat to move a distance D downstream?

Respuesta :

Answer:

Explanation:

Current  has speed vW with respect to the shore and boat has speed vB with respect to water or current so speed of boat  with respect to shore

vW + vB .

Distance travelled with respect to shore by boat = D

time ( tout ) = distance / speed with respect to shore

tOut = D / ( vW + vB )

When the boat travels upstream , its velocity with respect to shore

= ( vB - vW ) , vB must be higher .

tin = D /  ( vB - vW )

3 ) tin = D /  ( vB - vW )

170 = 120 / (vB - 0.3 )

(vB - 0.3 ) = 12 / 17 = .706

vB = 1.006 m / s

4 )

tOut = D / ( vW + vB )

= 120 / ( .3 + 1.006 )

= 92.26 s

Time taken by a body is ratio of the distance traveled by it to the speed.

  • 1)The expression for [tex]t{out}[/tex] is,

          [tex]t_{out}=\dfrac{D}{v_B+v_W}[/tex]

  • 2)The expression for [tex]t{in}[/tex] is,

           [tex]t_{in}=\dfrac{D}{v_B-v_W}[/tex]

  • 3) The speed of the boat with respect to the water is 1.006 m/s.
  • 4) The time it takes the boat to move a distance D downstream is 91.9 seconds.

What is upstream and downstream speed?

The net speed of the boat is upstream speed. The difference of the speed of the boat is downstream speed.

Given information-

The speed of the boat with respect to shore is [tex]v_w[/tex].

The speed of the boat in downstream with respect to water is [tex]v_B[/tex].

The distance traveled by the boat is [tex]D[/tex] in time [tex]t_{out}[/tex].

Time taken by a body is ratio of the distance traveled by it to the speed.

  • 1) The net speed of the boat is upstream speed.As the distance traveled by the boat is [tex]D[/tex] in time [tex]t_{out}[/tex]. Thus,

        [tex]t_{out}=\dfrac{D}{v_B+v_W}[/tex]

  • 2) The difference of the speed of the boat is downstream speed.As the distance traveled by the boat is [tex]D[/tex] in time [tex]t_{in}[/tex]. Thus,

        [tex]t_{in}=\dfrac{D}{v_B-v_W}[/tex]

Now the distance is 120 m, the value of [tex]t_{in}[/tex] is 170 s and [tex]v_W[/tex] 0.3 m/s. Thus,

  • 3) The speed of the boat with respect to the water-Put the values in the formula obtains from the 2nd part of the problem,

         [tex]170=\dfrac{120}{v_B-0.3}\\v_B-0.3=\dfrac{120}{160} \\v_B=0.706+0.3\\v_B=1.006[/tex]

Hence the speed of the boat with respect to the water is 1.006 m/s.

  • 4) The time it takes the boat to move a distance D downstream-Put the values in the formula obtains from the 1st part of the problem,

          [tex]t_{out}=\dfrac{120}{1.006+0.3}\\t{out}=\dfrac{120}{1.306} \\t{out}=91.9[/tex]

Hence the time it takes the boat to move a distance D downstream is 91.9 seconds.

Thus,

  • 1)The expression for [tex]t{out}[/tex] is,

          [tex]t_{out}=\dfrac{D}{v_B+v_W}[/tex]

  • 2)The expression for [tex]t{in}[/tex] is,

           [tex]t_{in}=\dfrac{D}{v_B-v_W}[/tex]

  • 3) The speed of the boat with respect to the water is 1.006 m/s.
  • 4) The time it takes the boat to move a distance D downstream is 91.9 seconds.

Learn more about the upstream and downstream speed here;

https://brainly.com/question/800251

Otras preguntas