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katen-ka-za [31]
3 years ago
14

In his​ motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing​ spot, a distance of 120120 ​mi, in 33 hr.

​ Returning, he finds that the trip​ downstream, still at top​ speed, takes only 2.52.5 hr. Find the rate of​ Bill's boat and the speed of the current. Let x​ = the rate of the boat in still water and y​ = the rate of the current.
Physics
1 answer:
photoshop1234 [79]3 years ago
8 0

Answer:

The rate of the boat in still water is 44 mph and the rate of the current is 4 mph

Explanation:

x​ = the rate of the boat in still water

y​ = the rate of the current.

Distance travelled = 120 mi

Time taken upstream = 3 hr

Time taken downstream = 2.5 hr

Speed = Distance / Time

Speed upstream

\frac{120}{3}=x-y\\\Rightarrow 40=x-y

Speed downstream

\frac{120}{2.5}=x+y\\\Rightarrow 48=x+y

Adding both the equations

48+40=x-y+x+y\\\Rightarrow 88=2x\\\Rightarrow 44=x

40=44-y\\\Rightarrow 40-44=-y\\\Rightarrow y=4

The rate of the boat in still water is <u>44 mph</u> and the rate of the current is <u>4 mph</u>

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Answer:

The maximum mass that can fall on the mattress without exceeding the maximum compression distance is 16.6 kg

Explanation:

Hi there!

Due to conservation of energy, the potential energy (PE) of the mass at a height of 3.32 m will be transformed into elastic potential energy (EPE) when it falls on the mattress:

PE = EPE

m · g · h = 1/2 k · x²

Where:

m = mass.

g = acceleration due to gravity.

h = height.

k = spring constant.

x = compression distance

The maximum compression distance is 0.1289 m, then, the maximum elastic potential energy will be the following:

EPE =1/2 k · x²

EPE = 1/2 · 65144 N/m · (0.1289 m)² = 541.2 J

Then, using the equation of gravitational potential energy:

PE = m · g · h =  541.2 J

m =  541.2 J/ g · h

m = 541.2 kg · m²/s² / (9.8 m/s² · 3.32 m)

m = 16.6 kg

The maximum mass that can fall on the mattress without exceeding the maximum compression distance is 16.6 kg.

6 0
3 years ago
It has been suggested that rotating cylinders about 10 mi long and 5.9 mi in diameter be placed in space and used as colonies. T
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Answer:

ω = 0.05 rad/s

Explanation:

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Centripetal Force = Weight\\\frac{mv^{2}}{r} = mg\\\\here,\\v = linear\ speed = r\omega \\therefore,\\\frac{(r\omega)^{2}}{r} = g\\\\\omega^{2} = \frac{g}{r}\\\\\omega = \sqrt{\frac{g}{r}}\\

where,

ω = angular velocity of cylinder = ?

g = required acceleration = 9.8 m/s²

r = radius of cylinder = diameter/2 = 5.9 mi/2 = 2.95 mi = 4023.36 m

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\omega = \sqrt{\frac{9.8\ m/s^{2}}{4023.36\ m}}\\\\

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gravitational force attract us towards the ground

Explanation:

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In the demolition of an old building, a 1,300 kg wrecking ball hits the building at 1.07 m/s2. Calculate the amount of force at
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Answer: F = 1391 N

Explanation:

The information given to you are:

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