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Marianna [84]
3 years ago
13

A boat heads directly across a river. Its speed relative to the water is 3 m/s. It takes it 539 seconds to cross, but it ends up

662 m downstream. How fast is the boat going relative to the bank of the river?
I dont know what i am doing wrong???
Physics
1 answer:
nikklg [1K]3 years ago
5 0

Answer:

3.24 m/s

Explanation:

Suppose that the boat sails with velocity (relative to water) direction being perpendicular to water stream. Had there been no water flow, it would have ended up 0m downstream

Therefore, the river speed is the one that push the boat 662 m downstream within 539 seconds. We can use this to calculate its magnitude

v_r = 662 / 539 = 1.23 m/s

So the boat velocity vector relative to the bank is the sum of of the boat velocity vector relative to the water and the water velocity vector relative to the bank. Since these 2 component vectors are perpendicular to each other, the magnitude of the total vector can be calculated using Pythagorean formula:

v = \sqrt{v_b^2 + v_r^2} = \sqrt{3^2 + 1.23^2} = \sqrt{9 + 1.5129} = \sqrt{10.5129} = 3.24 m/s

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SCALCET8 3.9.018.MI. A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the
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The length of his shadow is decreasing at a rate of 1.13 m/s

Explanation:

The ray of light hitting the ground forms a right angled triangle of height H, which is the height of the building and width, D which is the distance of the tip of the shadow from the building.

Also, the height of the man, h which is parallel to H forms a right-angled triangle of width, L which is the length of the shadow.

By similar triangles,

H/D = h/L

L = hD/H

Also, when the man is 4 m from the building, the length of his shadow is L = D - 4

So, D - 4 = hD/H

H(D - 4) = hD

H = hD/(D - 4)

Since h = 2 m and D = 12 m,

H = 2 m × 12 m/(12 m - 4 m)

H = 24 m²/8 m

H = 3 m

Since L = hD/H

and h and H are constant, differentiating L with respect to time, we have

dL/dt = d(hD/H)/dt

dL/dt = h(dD/dt)/H

Now dD/dt = velocity(speed) of man = -1.7 m/s ( negative since he is moving towards the building in the negative x - direction)

Since h = 2 m and H = 3 m,

dL/dt = h(dD/dt)/H

dL/dt = 2 m(-1.7 m/s)/3 m

dL/dt = -3.4/3 m/s

dL/dt = -1.13 m/s

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3 years ago
One of the main factors driving improvements in the cost and complexity of integrated circuits (ICs) is improvements in photolit
nika2105 [10]

Answer:

0.000003782 m

0.000001891 m

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f = Focal length = 0.625 cm

The angle is given by

\theta=\dfrac{1.22\lambda}{D}

The width is given by

d=2\theta f\\\Rightarrow d=2\dfrac{1.22\lambda f}{D}\\\Rightarrow d=2\dfrac{1.22\times 248\times 10^{-9}\times 6.25\times 10^{-2}}{1\times 10^{-2}}\\\Rightarrow d=0.000003782\ m

The required width is 0.000003782 m

Minimum resolvable line separation is given by

\dfrac{0.000003782}{2}=0.000001891\ m

The minimum resolvable line separation between adjacent lines is 0.000001891 m

when \lambda=157\ nm

d=2\dfrac{1.22\times 157\times 10^{-9}\times 6.25\times 10^{-2}}{1\times 10^{-2}}\\\Rightarrow d=0.00000239425\ m

The new minimum resolvable line separation between adjacent lines is

\dfrac{0.00000239425}{2}=0.000001197125\ m

6 0
3 years ago
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