Answer:
See the answers below
Explanation:
In this problem, we must be clear about the concept of weight. Weight is defined as the product of mass by gravitational acceleration.
We must be clear that the mass is always preserved, that is, the mass of 15 [kg] will always be the same regardless of the planet where they are.
where:
W = weight [N] (units of Newtons)
m = mass = 15 [kg]
g = gravity acceleration [m/s²]
Since we have 9 places with different gravitational acceleration, then we calculate the weight in each of these nine places.
<u>Mercury</u>
<u />![w_{mercury} = 15*3.8\\w_{mercury}= 57 [N]\\](https://tex.z-dn.net/?f=w_%7Bmercury%7D%20%3D%2015%2A3.8%5C%5Cw_%7Bmercury%7D%3D%2057%20%5BN%5D%5C%5C)
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<u>Venus</u>
<u />![w_{venus}=15*8.8\\w_{venus}= 132 [N]](https://tex.z-dn.net/?f=w_%7Bvenus%7D%3D15%2A8.8%5C%5Cw_%7Bvenus%7D%3D%20132%20%5BN%5D)
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<u>Moon</u>
<u />![w_{moon}=15*1.6\\w_{moon}=24[N]](https://tex.z-dn.net/?f=w_%7Bmoon%7D%3D15%2A1.6%5C%5Cw_%7Bmoon%7D%3D24%5BN%5D)
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<u>Mars</u>
![w_{mars}=15*3.7\\w_{mars}=55.5 [N]](https://tex.z-dn.net/?f=w_%7Bmars%7D%3D15%2A3.7%5C%5Cw_%7Bmars%7D%3D55.5%20%5BN%5D)
<u>Jupiter</u>
<u />![w_{jupiter}=15*23.1\\w_{jupiter}= 346.5[N]](https://tex.z-dn.net/?f=w_%7Bjupiter%7D%3D15%2A23.1%5C%5Cw_%7Bjupiter%7D%3D%20346.5%5BN%5D)
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<u>Saturn</u>
<u />![w_{saturn}=15*9\\w_{saturn}=135[N]](https://tex.z-dn.net/?f=w_%7Bsaturn%7D%3D15%2A9%5C%5Cw_%7Bsaturn%7D%3D135%5BN%5D)
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<u>Uranus</u>
<u />![w_{uranus}=15*8.7\\w_{uranus}=130.5[N]](https://tex.z-dn.net/?f=w_%7Buranus%7D%3D15%2A8.7%5C%5Cw_%7Buranus%7D%3D130.5%5BN%5D)
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<u>Neptune</u>
<u />![w_{neptune}=15*11\\w_{neptune}=165[N]](https://tex.z-dn.net/?f=w_%7Bneptune%7D%3D15%2A11%5C%5Cw_%7Bneptune%7D%3D165%5BN%5D)
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<u>Pluto</u>
<u />![w_{pluto}=15*0.6\\w_{pluto}=9[N]](https://tex.z-dn.net/?f=w_%7Bpluto%7D%3D15%2A0.6%5C%5Cw_%7Bpluto%7D%3D9%5BN%5D)
<u />
E=the sound waves from the trombones have slightly different velocity
First, we will get the resultant force:
The direction of the force due to the person's weight is vertically down.
weight of person = 700 newton
Assume that the force exerted by the arms has a vertically upwards direction.
Force exerted by arms = 2*355 = 710 newtons
Therefore, the resultant force = 710 - 700 = 10 newtons (in the vertically upwards direction)
Now, we will get the mass of the person.
weight = 700 newtons
weight = mass * acceleration due to gravity
700 = 9.8*mass
mass = 71.428 kg
Then we will calculate the acceleration of the resultant force:
Force = mass*acceleration
10 = 71.428*acceleration
acceleration = 0.14 m/sec^2
Finally, we will use the equation of motion to get the final speed of the person.
V^2 = U^2 + 2aS where:
V is the final velocity that we need to calculate
U is the initial velocity = 0 m/sec (person starts at rest)
a is the person's acceleration = 0.14 m/sec^2
S is the distance covered = 25 cm = 0.25 meters
Substitute with the givens in the above equation to get the final speed as follows:
V^2 = U^2 + 2aS
V^2 = (0)^2 + 2(0.14)(0.25)
V^2 = 0.07
V = 0.2645 m/sec
Based on the above calculations:
The person's speed at the given point is 0.2645 m/sec
