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Projectile5/1/2023 ![]() Projectile Motion- Examples Projectile Motion Example- Bullet shot by a gunīecause of the force supplied by the ignition of the gunpowder, a bullet shot from a gun travels a long distance. H = v 0 t h sinθ – 1/2 g t h 2 => h = (v 0 2 sin 2θ) / 2gįor θ=90°, the maximum achievable altitude is attained and is given by : h = (v 0 2) / 2g The magnitude of velocity (as determined by the Pythagorean theorem, often known as the triangle rule) is as follows:Īt any time (t ), the projectile’s displacements(x and y) in horizontal and vertical planes are given by: x = v 0 t cos ( θ ), y = v 0 t sin ( θ ) − 1/ 2 g t 2įor the displacement of the projectile’s greatest height: The following are the components of the acceleration: a x = 0, a y = – g The acceleration is constant in this case, equal to g. The projectile’s vertical motion is the motion of a particle in free fall. The velocity in the horizontal plane is static, equal to v 0 cos, because there is only acceleration in the vertical plane. The trajectory can be circular, parabolic, or hyperbolic at higher speeds (unless distorted by other objects like the Moon or the Sun). If an object were thrown and the Earth was replaced with a black hole of similar mass, it would be clear that the ballistic trajectory is part of an elliptic orbit around the black hole, not a parabola that continues to infinity. On a small scale, this results in an elliptic trajectory that is remarkably similar to a parabola. On Earth, the amplitude and direction of acceleration change with altitude and latitude/longitude. In the absence of extraneous forces, a ballistic trajectory is a parabola with homogenous acceleration, such as in a spaceship with constant acceleration.
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