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Newton's first law is often referred to as the law of inertia. Thus, a condition necessary for the uniform motion of a particle relative to an inertial reference frame is that the total net force acting on it is zero. In this sense, the first law can be restated as:
In every material universe, the motion of a particle in a preferential reference frame Φ is determined by the action of forces whose total vanished for all times when and only when the velocity of the particle is constant in Φ. That is, a particle initially at rest or in uniform motion in the preferential frame Φ continues in that state unless compelled by forces to change it.
Newton's laws are valid only in an inertial reference frame. Any reference frame that is in uniform motion with respect to an inertial frame is also an inertial frame
Time of flight = 2·V·sinΘ/g = 1.60 s ← #1
range = (V²sin(2Θ))/g = 0.75 m ← #2
Divide #2 by #1:
0.75m / 1.6s = Vsin(2Θ) / 2sinΘ
But sin(2Θ)= 2sinΘcosΘ, so
0.47 m/s = VcosΘ ← initial horizontal component -- #3
rearranges to V = 0.47m/s / cosΘ
Now plug that into #1:
2 * (0.47m/s / cosΘ) * sinΘ / 9.8m/s² = 1.6 s
0.096s * tanΘ = 1.6s
tanΘ = 16.7
Now multiply both sides of #3 by tanΘ = 16.7
0.47m/s * 16.7 = VcosΘ * tanΘ = VsinΘ
VsinΘ = 7.8 m/s ← vertical component
Note that we don't need to know either the angle or the initial velocity; we just need the vertical component (VsinΘ) and the horizontal component (VcosΘ).
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