# tell about projectile launched from height

Suraj Prasad IIT Patna
askIITians Faculty 286 Points
8 years ago
In physics, assuming a flat Earth with a uniform gravity field, and no air resistance, a projectile launched with specific initial conditions will have a predictable range.

The following applies for ranges which are small compared to the size of the Earth. For longer ranges see sub-orbital spaceflight. The maximum horizontal distance traveled by the projectile

g: the gravitational acceleration—usually taken to be 9.81m/s2 (32 f/s2) near the Earth's surface
θ: the angle at which the projectile is launched
v: the velocity at which the projectile is launched
y0: the initial height of the projectile
d: the total horizontal distance travelled by the projectile

When neglecting air resistance, the range of a projectile will be

[d = \frac{v \cos \theta}{g} \left( v \sin \theta + \sqrt{v^2 \sin^2 \theta + 2gy_0} \right)]

If (y0) is taken to be zero, meaning the object is being launched on flat ground, the range of the projectile will then simplify to

[d = \frac{v^2}{g} \sin(2\theta)]