You are designing an apparatus to shoot a water balloon through a 3rd story window (25m above the ground)

The balloon needs a vertical velocity of approximately 22.14 m/s to reach the window

Explanation:

The given parameters are;

The destination of the designed water balloon we shoot = The 3rd story window

The height of the 3rd story window which the water balloon should reach = 25 m

Therefore, we have, the equation of motion of the water balloon given as follows;

v² = u² - 2 × g × s

Where;

= The initial vertical velocity of the balloon

= The final vertical velocity of the balloon = 0 m/s

g = The acceleration due to gravity = 9.8 m/s

s = The height the balloon is intended reach at the final velocity becomes 0 m/s = The height of the 3rd story window

∴ s = 25 m

Substituting the values, we have;

0² = ² - 2 × 9.8 × 25

² = 2 × 9.8 × 25 = 490

= √490 = 7·√10

The initial vertical velocity of the balloon = = 7·√10 m/s

Therefore, the balloon needs a vertical velocity of 7·√10 m/s which is approximately 22.14 m/s to reach the window.

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