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As a spacecraft approaches the planet Jupiter, it releases a probe which is to enter the planet's atmosphere at point $B$ at an altitude of $280 \mathrm{mi}$ above the surface of the planet. The trajectory of the probe is a hyperbola of eccentricity $e=1.031$. Knowing that the radius and the mass of Jupiter are $44,423 \mathrm{mi}$ and $1.30 \times 10^{26}$ slug, respectively, and that the velocity $\mathbf{v}_{B}$ of the probe at $B$ forms an angle of $82.9^{\circ}$ with the direction of $O A$, determine $(a)$ the angle $A O B,(b)$ the speed $v_{B}$ of the probe at $B$
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Physics 101 Mechanics
Chapter 12
Kinetics of Particles: Newton’s Second Law
Newton's Laws of Motion
University of Michigan - Ann Arbor
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University of Sheffield
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Lectures
03:28
Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.
09:37
Isaac Newton (4 January 1643 – 31 March 1727) was an English mathematician, physicist, astronomer, theologian, and author (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.
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