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Vacuum trajectory of a projectile for different launch angles. Launch speed is the same for all angles, 50 m/s, and "g" is 10 m/s 2. To hit a target at range x and altitude y when fired from (0,0) and with initial speed v the required angle(s) of launch θ are:
A launch angle of 45 degrees displaces the projectile the farthest horizontally. This is due to the nature of right triangles. Additionally, from the equation for the range :
To find the angle giving the maximum height for a given speed calculate the derivative of the maximum height = / with respect to , that is = / which is zero when = / =. So the maximum height H m a x = v 2 2 g {\displaystyle H_{\mathrm {max} }={v^{2} \over 2g}} is obtained when the projectile is fired straight up.
Plot of trajectories of projectiles launched at different elevation angles but the same speed of 10 m/s in a vacuum and uniform downward gravity of 10 m/s^2; t = time from launch, T = time of flight, R = range and H = highest point of trajectory (indicated with arrows); points are at 0.05 s intervals and length of their tails is linearly ...
The downward swing path, impact, club face angle, launch angle and ball speed are all captured by the high speed cameras, normally running at around 100 to 120 frames per second. Camera data is processed using complex physics algorithms to produce a multitude of data such as back spin, side spin, trajectory, club face angle, swing path, loft ...
The planet-fixed values of v and θ are converted to space-fixed (inertial) values with the following conversions: [7] = + + (), where ω is the planet's rotational rate in radians per second, φ is the launch site latitude, and A z is the launch azimuth angle.
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For projectiles in unpowered flight, its velocity is highest at leaving the muzzle and drops off steadily because of air resistance.Projectiles traveling less than the speed of sound (about 340 m/s (1,100 ft/s) in dry air at sea level) are subsonic, while those traveling faster are supersonic and thus can travel a substantial distance and even hit a target before a nearby observer hears the ...