# Equation of trajectory for a projectile is y = 2x{1-(x/40)} (where x and y are in meter). What will be the range of the projectile?

##### 1 Answer

Let the velocity of projection of the projectile in x-y plane from the origin (0,0) be **u** with angle of projection

The vertical component of the velocity (along y-axis) of projection is

Now if the time of flight be **T** then the object will return to the ground after T sec and during this T sec its total vertical displacement **h** will be zero. So applying the equation of motion under gravity we can write

where

The horizontal displacement during this T sec or the **Range** ,

Let the position of the projectile in x-y plane after t sec of its projection be

The horizontal displacement during t sec

And the vertical displacement during t sec

Combining (1) and (2) we get

This is the equation of the trajectory,we obtained.

Now in the given problem the equation of the trajectory is

Comparing (4) and (5) we get

and

Multiplying (6) by (7) we get

So Range of the projectile