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==Equations of motion== {{main|Projectile motion}} An object projected at an angle to the horizontal has both the vertical and horizontal components of velocity. The vertical component of the velocity on the y-axis is given as <math>V_y=U\sin\theta</math> while the horizontal component of the velocity is <math>V_x=U\cos\theta</math>. There are various calculations for projectiles at a specific angle <math>\theta</math>: 1. Time to reach maximum height. It is symbolized as (<math>t</math>), which is the time taken for the projectile to reach the maximum height from the plane of projection. Mathematically, it is given as <math>t=U \sin\theta/g</math> where <math>g</math> = acceleration due to gravity (app 9.81 m/sΒ²), <math>U</math> = initial velocity (m/s) and <math>\theta</math> = angle made by the projectile with the horizontal axis. 2. Time of flight (<math>T</math>): this is the total time taken for the projectile to fall back to the same plane from which it was projected. Mathematically it is given as <math>T=2U\sin\theta/g</math>. 3. Maximum Height (<math>H</math>): this is the maximum height attained by the projectile OR the maximum displacement on the vertical axis (y-axis) covered by the projectile. It is given as <math>H = U^2 \sin^2\theta/2g</math>. 4. Range (<math>R</math>): The Range of a projectile is the horizontal distance covered (on the x-axis) by the projectile. Mathematically, <math>R = U^2 \sin 2\theta/g</math>. The Range is maximum when angle <math>\theta</math> = 45Β°, i.e. <math>\sin 2\theta=1</math>.
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