Projectile motion is a type of motion in which an object is thrown near the earth's surface and moves along a curved path under the influence of gravity only. In this motion, the object has both horizontal and vertical components of motion.


When a body is projected with a speed u at an angle to the horizontal to have maximum range, the angle of projection is 45 degrees. At this angle, the horizontal range of the projectile is maximum.


At the highest point of the projectile's motion, the vertical component of the velocity becomes zero. However, the horizontal component of the velocity remains constant throughout the motion. Therefore, the velocity at the highest point is equal to the horizontal component of the initial velocity.


When a body is projected at an angle to the horizontal, the initial velocity can be resolved into horizontal and vertical components. The horizontal component remains constant throughout the motion, while the vertical component changes due to the acceleration due to gravity. At the highest point of the motion, the vertical component of the velocity becomes zero, but the horizontal component remains constant. Therefore, the velocity at the highest point is equal to the horizontal component of the initial velocity.


In conclusion, when a body is projected with a speed u at an angle to the horizontal to have maximum range, the velocity at the highest point is equal to the horizontal component of the initial velocity. This is because the horizontal component of the velocity remains constant throughout the motion, while the vertical component becomes zero at the highest point.

Maximum range means, angle=45`
total velocity=vertical velocity (0) +horizontal velocity(Vcos45)
=V√2