Question

Water from a sprinkler comes out with a constant velocity 'u' in all directions. What is maximum area of grassland that can be watered at any time?

Answer 1

Maximum distance will be at angle 45°
distance = (v²sin2α)/g
radius= u²/g units
now, area = π(u²/g)² = π(u^4)/g²

Answer 2

Given :

Velocity of water from the sprinkler = u

To Find :

The maximum area of grassland that can be watered

Solution :

• The water from the sprinkler travels in all directions in the projectile motion
• The maximum range of the water is equal to radius of the circular area that can be watered

           $Maximum\:range=\frac{u^{2}}{g}$

           $r=\frac{u^{2} }{g}$

• The circular area that can be watered = $\pi r^{2}$

           $A=\pi r^{2}$

           $A=\pi (\frac{u^{2} }{g})^{2}$

           $A = \pi \frac{u^{4}}{g^{2}}$

The maximum area of grassland that can be watered is  $A = \pi \frac{u^{4}}{g^{2}}$