An object in space is initially stationary relative to the Earth. Then, a force begins acting on the object, starting with a for
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The largest mass is 4.7 x 10³⁰ kg and the smallest mass is 5 x 10²⁹ kg.
The given parameters;
- <em>distance between the two black holes, r = 10 AU = 1.5 x 10¹² m</em>
- <em>gravitational force between the two black holes, F = 6.9 x 10²⁵ N.</em>
- <em>combined mass of the two black holes = 5.20 x 10³⁰ kg</em>
The product of the two masses is calculated from Newton's law of universal gravitational as follows;
The sum of the two masses is given as;
m₁ + m₂ = 5.2 x 10³⁰ kg
m₂ = 5.2 x 10³⁰ kg - m₁
The first mass is calculated as follows;
m₁(5.2 x 10³⁰ - m₁) = 2.328 x 10⁶⁰
5.2 x 10³⁰m₁ - m₁² = 2.328 x 10⁶⁰
m₁² - 5.2 x 10³⁰m₁ + 2.328 x 10⁶⁰ = 0
<em>solve the quadratic equation using formula method</em>;
a = 1, b =- 5.2 x 10³⁰, c = 2.328 x 10⁶⁰
The second mass is calculated as follows;
m₂ = 5.2 x 10³⁰ kg - m₁
m₂ = 5.2 x 10³⁰ kg - 4.7 x 10³⁰ kg
m₂ = 5 x 10²⁹ kg
or
m₂ = 5.2 x 10³⁰ kg - 4.9 x 10²⁹ kg
m₂ = 4.7 x 10³⁰ kg
Thus, the largest mass is 4.7 x 10³⁰ kg and the smallest mass is 5 x 10²⁹ kg.
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Answer:
Given:
Initial speed (u) = 10 m/s
Acceleration (a) = 2 m/s²
Time taken (t) = 3s
To Find:
Final speed (v) of the car
Explanation:
From equation of motion we have:
By substituting value of u, a & t in the equation we get:
Final speed (v) of the car = 16 m/s