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Anastaziya [24]
3 years ago
15

The astronaut then measures the abundance of silicon on the new planet, obtaining the following results: Isotope Abundance. (%)M

ass. (amu). 28Si73.7127.98. 29Si14.9328.98. 30Si11.3629.97. What is the atomic mass of silicon for this planet?
Physics
1 answer:
tekilochka [14]3 years ago
5 0
<span>In order to calculate an average, we should sum all numbers and divide them by quantity. Let’s work with qualifications first. Let’s say you got a 10 in 1 exam, then an 8 in 2 exams and a 4 in 2 exams. Your average will be: = (10*1+8*2+4*2) / 5 = 6.8 If 6 is the minimum, you will pass. There is another way to calculate this average: applying distributive property. = 10*1/5+8*2/5+4*2/5 = 6.8 Remember you can convert the fractions into equivalent fractions: 1/5 = 20/100; 2/5 = 40/100 = 10*20/100+8*20/100+4*20/100 = 6.8 We actually don’t have the number of atoms of each mass… we have the percentage instead! So we need to learn this last method for atoms. Let’s go back to our atoms problem: 73.71 % of atoms have a mass of 27.98 u 14.93 % of atoms have a mass of 28.98 u 11.36 % of atoms have a mass of 29.97 u So let’s put that in the formula: Average mass = 27.98 u*73.71 /100 + 28.98 u*14.93 /100 + 29.97u*11.36 /100 So what you have to know is that a percentage can be converted into a fraction, and you should work that fraction in order to find the average. We can make the calculus shorter putting 100 as the common denominator: Average mass = (27.98 u*73.71 + 28.98 u*14.93 + 29.97u*11.36)/100 So actually we are taking the percentage as if it was the quantity, and 100 as if it was the total (the total of all percentages is always 100). Maybe we don’t have 100 atoms, but it will be the same proportion anyway, whatever number we have! And here it is the result: Average mass = 28,36u </span>
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Answer:

His launching angle was 14.72°

Explanation:

Please, see the figure for a graphic representation of the problem.

In a parabolic movement, the velocity and displacement vectors are two-component vectors because the object moves along the horizontal and vertical axis.

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sin angle = v0y / v0  then: v0y = v0 * sin angle

In the same way for vx:

vx = v0 * cos angle

Using the equation for velocity in the x-axis we can find the equation for the horizontal position:

dx / dt = v0 * cos angle

dx = (v0 * cos angle) dt (integrating from initial position, x0, to position at time t and from t = 0 and t = t)

x - x0 = v0 t cos angle

x = x0 + v0 t cos angle

For the displacement in the y-axis, the velocity is not constant because the acceleration of the gravity:

dvy / dt = g ( separating variables and integrating from v0y and vy and from t = 0 and t)

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The position will be:

dy/dt = v0 * sin angle + g t

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y = y0 + v0 t sin angle + 1/2 g t²

The displacement vector at a time "t" will be:

r = (x0 + v0 t cos angle, y0 + v0 t sin angle + 1/2 g t²)

If the launching and landing positions are at the same height, then the displacement vector, when the object lands, will be (see figure)

r = (x0 + v0 t cos angle, 0)

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-65m (sin angle / cos angle) = 1/2 g * (65m)² / (v0² cos² angle)  

using g = -9.8 m/s²

-(sin angle / cos angle) * (cos² angle) = -318.5 m²/ s² / v0²

sin angle * cos angle = 318.5 m²/ s² / (36 m/s)²

(using trigonometric identity: sin x cos x = sin (2x) / 2

sin (2* angle) /2 = 0.25

sin (2* angle) = 0.49

2 * angle = 29.44

<u>angle = 14.72°</u>

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