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sveticcg [70]
2 years ago
8

A lighthouse is located on a small island, 3 km away from the nearest point on a straight shoreline, and its light makes four re

volutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from ?

Physics
1 answer:
lbvjy [14]2 years ago
7 0

Answer:

The beam of light is moving at the peed of:

\frac{dy}{dt} = \frac{80\pi}{3} km/min

Given:

Distance from the isalnd, d = 3 km

No. of revolutions per minute, n = 4

Solution:

Angular velocity, \omega = \frac{d\theta'}{dt} = 2\pi n = 2\pi \times 4 = 8\pi    (1)

Now, in the right angle in the given fig.:

tan\theta' = \frac{y}{3}

Now, differentiating both the sides w.r.t t:

\frac{dtan\theta'}{dt} = \frac{dy}{3dt}

Applying chain rule:

\frac{dtan\theta'}{d\theta'}.\frac{d\theta'}{dt} = \frac{dy}{3dt}

sec^{2}\theta'\frac{d\theta'}{dt} = \frac{dy}{3dt} = (1 + tan^{2}\theta')\frac{d\theta'}{dt}

Now, using tan\theta = \frac{1}{m} and y = 1 in the above eqn, we get:

(1 + (\frac{1}{3})^{2})\frac{d\theta'}{dt} = \frac{dy}{3dt}

Also, using eqn (1),

8\pi\frac{10}{9})\theta' = \frac{dy}{3dt}

\frac{dy}{dt} = \frac{80\pi}{3}

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Beams used in Heavy Timber construction are sometimes firecut. This is done to: a) allow air circulation at the beam’s end in an
ladessa [460]

Answer:

option C

Explanation:

The correct answer is option C

Fire cut of fireman cut is diagonal cut which is provided at the end of the beam to prevent the fall of masonry wall if a fire breaks out in the building.

Fire cut allows joist to leave if it fails without affecting the masonry wall standing.

Without fire cut, the burnt beam will rotate downward affecting the connection of beam and wall and leading to damage it.

8 0
3 years ago
roblem 10: In an adiabatic process oxygen gas in a container is compressed along a path that can be described by the following p
miskamm [114]

Answer:

W= -2.5 (p₁*0.0012) joules

Explanation:

Given that p₀= initial pressure, p₁=final pressure, Vi= initial volume=0 and Vf=final volume= 6/5 liters where p₁=p₀ then

In adiabatic compression, work done by mixture during compression is

W= \int\limits^f_i {p} \, dV  where f= final volume and i =initial volume, p=pressure

p can be written as p=K/V^γ where K=p₀Vi^γ =p₁Vf^γ

W= \int\limits^f_i {K/V^} \, dV

W= K/1-γ ( 1/Vf^γ-1 - 1/Vi^γ-1)

W=1/1-γ (p₁Vf-p₀Vi)

W= 1/1-1.40 (p₁*6/5 -p₀*0)  

W= -2.5 (p₁*6/5*0.001)   changing liters to m³

W= -2.5 (p₁*0.0012) joules

3 0
2 years ago
Which muscle is the main muscle of mastication?
Valentin [98]

Answer: Masseter muscle

Explanation:

The masseter muscle is the most powerful muscle of mastication. It is quadrangular in shape and has two parts: deep and superficial. The entirety of the muscle lies superficially to the pterygoids and temporalis, covering them.

4 0
3 years ago
6) What force should be applied to compress a spring
valina [46]

Answer:

26.6N

Explanation:

Using Hooke’s law

F = kx

Where F = force

K = spring constant

x = displacement

From the question

F= ?

K = 140 N/m

x = 0.19m

Therefore,

F = 140 x 0.19

= 26.6N

7 0
2 years ago
HELP PLEASE!!!!
olganol [36]

The distance travelled by the ball is 43.2 m

Explanation:

The motion of the ball is a projectile motion, which consists of two independent motions:  

- A uniform motion (constant velocity) along the horizontal direction  

- A uniformly accelerated motion, with constant acceleration (acceleration of gravity) in the downward direction  

Here, we want to find the (horizontal) distance travelled by the ball before hitting the ground. Therefore, we can just consider the horizontal motion of the ball.

Since it is a uniform motion, we can write:

v=\frac{d}{t}

where

v = 13.5 m/s is the horizontal speed

t = 3.2 s is the time of flight

Solving for d, we find

d=vt=(13.5)(3.2)=43.2 m

Learn more about projectile motion:

brainly.com/question/8751410

#LearnwithBrainly

7 0
3 years ago
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