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AnnZ [28]
2 years ago
5

A 0.14-km wide river flows with a uniform speed of 4.0 m/s toward the east. It takes 20 s for a boat to cross the river to a poi

nt directly north of its departure point on the south bank. What is the speed of the boat relative to the water
Physics
1 answer:
Dmitry [639]2 years ago
7 0

Answer:

The right approach is "8.1 m/s". A further explanation is provided below.

Explanation:

According to the table,

Speed of Boat

= \frac{s}{t}

V_b=\frac{140}{20}

V_a = 4 \ m/s

V_B = 7 \ m/s

Now,

⇒  (V_{relative})^2 = (7)^2+(4)^2

or,

⇒  (V_r)^2=49+16

              =65

         V_r=\sqrt{65}

              =8.1 \ m/s

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2 years ago
A 1.8 kg uniform rod with a length of 90 cm is attached at one end to a frictionless pivot. It is free to rotate about the pivot
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a. 32.67 rad/s²  b. 29.4 m/s²

Explanation:

a. The initial angular acceleration of the rod

Since torque τ = Iα = WL (since the weight of the rod W is the only force acting on the rod , so it gives it a torque, τ at distance L from the pivot )where I = rotational inertia of uniform rod about pivot = mL²/3 (moment of inertia about an axis through one end of the rod), α = initial angular acceleration, W = weight of rod = mg where m = mass of rod = 1.8 kg and g = acceleration due to gravity = 9.8 m/s² and L = length of rod = 90 cm = 0.9 m.

So, Iα = WL

mL²α/3 = mgL

dividing through by mL, we have

Lα/3 = g

multiplying both sides by 3, we have

Lα = 3g

dividing both sides by L, we have

α = 3g/L

Substituting the values of the variables, we have

α = 3g/L

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= 29.4/0.9 rad/s²

= 32.67 rad/s²

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