MAXIMUM HEIGHT
 
 
Maximum height of the projectile occurs when the vertical component of velocity (Voy=Vf) becomes zero. Suppose T be the time when the vertical component of velocity reduces to zero and Y=h be the maximum height, then,we have:
Which is the expression for maximum height
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HORIZONTAL RANGE OF PROJECTILE
 
The horizontal distance covered by the projectile during its complete flight is called its range and is denoted by 'R'. in order to find the range of the projectile we make use of the fact that the total flight requires a time that is t = 2T. As the horizontal component of velocity remains uniform, the range can be determined by
MAXIMUM RANGE
 
The range of a projectile is max. when sin2q is maximum and the max. value of sin2q is unity.
i.e. R=Rmax
if sin2
q=1
since horizontal range is

R = Vo2 sin2
q/g
Therefore,
Rmax = Vo2 (1)/g
Rmax = Vo2 /g
Since,
sin2
q=1
2
q=sin-1(1)
2
q=90o
q=45o

This shows that the projectile must be launched at an angle of 45O to get maximum range.
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