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Ratling [72]
4 years ago
12

Astronaut Sarah leaves Earth in a spaceship at a speed of 0.280c relative to Earth. Sarah's destination is a star-system 12.5 li

ght-years away (one light-year is the distance light travels in one year). According to Sarah, how far did she travel during the trip?
Physics
1 answer:
Usimov [2.4K]4 years ago
8 0

Answer:

L= 12 light years

Explanation:

for length dilation we use the formula

L=L_0\sqrt{1-\frac{v^2}{c^2} }

now calculating Lo

Lo = 12.5×365×24×3600×3×10^8

= 1.183×10^17 m

now putting the values of v and Lo in the above equation we get

L=1.183\times10^{17}\sqrt{1-\frac{0.28c^2}{c^2} }

= 1.136×10^17 m

L=  = \frac{1.136\times10^{17}}{365\times24\times3600\times3\times10^8}m

so L= 12 light years

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A rope is tied to a tree 4.5 feet from the ground and then run through a pulley hooked to a vehicle 33 feet from the tree. If a
Angelina_Jolie [31]

Answer:

The vehicle displacement is 9.90 feet.

Explanation:

Given that,

Height of tree = 4.5 feet

Distance = 33 feet

According to figure,

We need to calculate the value of l

Using Pythagorean theorem

l=\sqrt{(33)^2+(4.5)^2}

We need to calculate the vehicle displacement

Using horizontal component

Vehicle displacement =horizontal component of pulled rope

Vehicle\ displacement= d\cos\theta

Where, \theta is angle between rope and ground

d = pulled length of rope

Vehicle\ displacement=10\times\dfrac{33}{\sqrt{(33)^2+(4.5)^2}}

Vehicle\ displacement=9.90\ feet

Hence, The vehicle displacement is 9.90 feet.

3 0
3 years ago
it took 3.5 hours for a train to travel the distance between two cities at a velocity of 120 miles per hour. How many miles lie
Art [367]

Given:

Time: 3.5 hrs

Velocity: 120 miles/hr

Now Distance=  Speed × Time

Now Velocity and speed have the same magnitude. Velocity being a vector quantity has a definite direction. Whereas speed is a scalar quantity,it indicates only the magnitude an doesn't define any direction.

Hence Distance = Velocity x time

Distance = 3.5 × 120 = 420 miles

7 0
3 years ago
Juan lives 100 m away from Bill.What is Juan's averege speed if he reaches Bill's home in 50 s?
Tom [10]
Juan lives a hundred miles away from Bill then the average speed that he reaches Bill's Home in 50 seconds means that Juan lives 50 seconds away from bill because 50 + 50 seconds equals 100 seconds so Juansorry my bad Juan lives 50 miles away from Belle but he probably how I must have run to get to bill in 50 seconds .
7 0
3 years ago
A 2,700-kg truck runs into the rear of a 1,000-kg car that was stationary. The truck and car are locked together after the colli
Leto [7]

Answer:

6200 J

Explanation:

Momentum is conserved.

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

The car is initially stationary.  The truck and car stick together after the collision, so they have the same final velocity.  Therefore:

m₁ u₁ = (m₁ + m₂) v

Solving for the truck's initial velocity:

(2700 kg) u = (2700 kg + 1000 kg) (3 m/s)

u = 4.11 m/s

The change in kinetic energy is therefore:

ΔKE = ½ (m₁ + m₂) v² − ½ m₁ u²

ΔKE = ½ (2700 kg + 1000 kg) (3 m/s)² − ½ (2700 kg) (4.11 m/s)²

ΔKE = -6200 J

6200 J of kinetic energy is "lost".

3 0
3 years ago
Each second, 1250 m3 of water passes over a waterfall 150 m high. Three-fourths of the kinetic energy gained by the water in fal
mote1985 [20]

Answer:

The generator produces electrical energy at a rate of 1378125000 J per second.

Explanation:

volume of water falling each second is 1250 m^{3}

height through which it falls, h is 150 m

mass of 1 m^{3} of water is 1000 kg

⇒mass of 1250 m^{3} of water, m = 1250×1000 = 1250000 kg

acceleration due to gravity, g = 9.8 \frac{m}{sec^{2} }

in falling through 150 m in each second, by Work-Energy Theorem:

Kinetic Energy(KE) gained by it = Potential Energy(PE) lost by it

⇒KE = mgh

        = 1250000×9.8×150 J

        = 1837500000 J

Electrical Energy = \frac{3}{4}(KE)

                            = \frac{3}{4}×1837500000

                            = <u>1378125000 J per second</u>

8 0
3 years ago
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