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