a projectile is fired from ground level with velocity 500 m/s at 30 degree to the horizontal . find its horizontal range ,the greatest vertical height to which it rises and the time to reach the greatest height .what is the least speed with which it could be projected in order to achieve the same horizontal range ? the resistance of air to the motion of the projectile may be neglected .given :g = 10 metre second square .

Dear Student ,
Here in this case the projectile is fired from ground level with velocity 500 m/s and at 300 with the horizontal .
Now the horizontal range is ,R=u2sin2αg=5002×sin60°10=21650·63 m=21·65 kmThe greatest vertical height to which it rises is ,H=u2sin2α2g=5002×(sin30°)210=6250 m=6·25 kmNow the time taken to reach the greatest height is ,T=u sinαg=500×sin30°10=25 seconds
Regards

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