Derive an expression for time of flight , horizontal range, maximum height for a body being projected at an angle to the horizontal. Also prove that there are two angle's of projection for which the horizontal range is same.
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At what angle to the horizontal should a body be projected so that the maximum height reached is equal to the horizontal range?
If the angle of projection is 75.96 degrees the maximum height is equal to the horizontal range.
How do you find the horizontal range of a projectile?
The range (R) of the projectile is the horizontal distance it travels during the motion. Using this equation vertically, we have that a = -g (the acceleration due to gravity) and the initial velocity in the vertical direction is usina (by resolving). Hence: y = utsina - ½ gt2 (1)
What is horizontal range in projectile motion?
The horizontal range of a projectile is the distance along the horizontal plane it would travel, before reaching the same vertical position as it started from. The horizontal range depends on the initial velocity v0, the launch angle θ, and the acceleration due to gravity. The unit of horizontal range is meters (m).