JUST KNOW! Why Does 45 Degrees Give The Maximum Range
The reason is calculus. Clearly from trigonometry we know that the maximum value of sin theta1 and we know that sin 9001 So in this case we have 2theta_0900 qquad orqquad theta_0450 Thus the horizontal range of a projectile for a given initial velocity is maximum when it is projected at an angle of 450 with the horizontal.
Maximum Range In Projectile Motion Wired
Sin45 Cos45.
Why does 45 degrees give the maximum range. The ideal theta is 45 degrees because this is the perfect compromise between flight time y-comp and horizontal speed x-comp. It only does in a vacuum. At Cos 01 you have.
If you express the range as a function of launch angle then you can differentiate it and find that the function takes a maximum value at 45.
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