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algol [13]
3 years ago
11

An asteroid orbiting the Sun has a mass of 4.00×1016 kg. At a particular instant, it experiences a gravitational force of 3.14×1

013 N from the Sun. The mass of the Sun is 1.99×1030 kg. How far is the asteroid from the Sun?
Physics
1 answer:
Ksivusya [100]3 years ago
3 0
<h2>The asteroid is 4.11 x 10¹¹ m far from Sun</h2>

Explanation:

We have gravitational force

                 F=\frac{GMm}{r^2}

           Where G =  6.67 x 10⁻¹¹ N m²/kg²

                       M = Mass of body 1

                       M = Mass of body 2

                       r = Distance between them

Here we have

                 M = Mass of Sun = 1.99×10³⁰ kg

                 m = Mass of asteroid = 4.00×10¹⁶ kg

                 F = 3.14×10¹³ N

Substituting

                   F=\frac{GMm}{r^2}\\\\3.14\times 10^{13}=\frac{6.67\times 10^{-11}\times 1.99\times 10^{30}\times 4\times 10^{16}}{r^2}\\\\r=4.11\times 10^{11}m

The asteroid is 4.11 x 10¹¹ m far from Sun

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<h3>Deniel's average speed for the total</h3><h3>distance is 3.6 mph</h3>

Average speed is difined as the total distance travelled divided by the total time required to cover the distance. Mathematically, it is expressed as:

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To obtain the average speed of Daniel, we shall determine the distance travelled in each case. This is illustrated below:

<h3>Case 1:</h3>

Speed 1 (S₁) = 6 mph

Time 1 (t₁) = 0.8 h.

<h3>Distance 1 (D₁) =? </h3>

Speed = \frac{Distance}{Time} \\\\S_{1}  = \frac{D_{1}}{t_{1}} \\\\6 = \frac{D_{1}}{0.8}

Cross multiply

D₁ = 6 × 0.8

<h3>D₁ = 4.8 mile</h3>

<h3>Case 2:</h3>

Speed 2 (S₂) = 2 mph

Time 2 (t₂) = 1.2 h.

<h3>Distance 2 (D₂) =? </h3>

S_{2} = \frac{D_{2}}{t_{2}}\\\\2 = \frac{D_{2}}{1.2}

Cross multiply

D₂ = 2 × 1.2

<h3>D₂ = 2.4 mile </h3>

Next, we shall determine the total time. This can be obtained as follow:

Time 1 (t₁) = 0.8 h.

Time 2 (t₂) = 1.2 h.

<h3>Total time (T) =? </h3>

T = t₁ + t₂

T = 0.8 + 1.2

<h3>T = 2 h</h3>

Next, we shall determine the total distance. This can be obtained as follow:

Distance 1 (D₁) = 4.8 mile

Distance 2 (D₂) = 2.4 mile

<h3>Total distance (D) =?</h3>

D = D₁ + D₂

D = 4.8 + 2.4

<h3>D = 7.2 mile</h3>

Finally, we shall determine the average speed of Daniel. This can be obtained as follow:

Total time = 2 h

Total distance  = 7.2 mile

<h3>Average speed =?</h3>

Ave. speed = \frac{Total distance }{Total time} \\\\Ave. speed = \frac{7.2 }{2}

<h3>Average speed = 3.6 mph</h3><h3 />

Therefore, the average speed of Daniel is 3.6 mph

Learn more: brainly.com/question/680492

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