What launch angle will give an object the maximum horizontal distance when projected?

The launch angle that gives an object the maximum horizontal distance when projected is 45 degrees. This angle allows for an optimal balance between the vertical and horizontal components of the projectile's motion.

At 45 degrees, the sine and cosine functions, which are used to calculate the vertical and horizontal components of the initial velocity, are equal. This maximizes the range because the object can achieve a high enough altitude to stay in the air longer while also covering a significant horizontal distance.

If the angle is less than 45 degrees, there is a greater emphasis on horizontal velocity, but the time spent in the air is less, which reduces the overall range. Conversely, if the angle is greater than 45 degrees, the vertical component increases at the expense of the horizontal distance, leading to less range. Thus, 45 degrees is the ideal angle for achieving the maximum horizontal distance.