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Question

# Consider a horizontally oriented syringe containing water whose nozzle is located at a height of 20 m above the ground. The diameter of the plunger is 10 mm and the diameter of the nozzle is 5 mm. The plunger is pushed with a constant speed of 1 m/s. Horizontal range of the water stream on the ground (in meters) is

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Solution

## Let us suppose, speed with which water comes out of the nozzle is v and horizontal range of water stream on the ground is d. According to question: On applying equation of continuity A1v1=A2v2 ⇒πd214v1=πd224v2 ⇒v2=(d1d2)2v1 ⇒v=(105)2×1 ⇒v=4 m/s ............(1) For vertical motion of water, on applying s=ut+12at2 Initial vertical component of velocity of water is zero ∴−20=12×−10×t2 [taking downward positive] ⇒t=2 s ... (2) For horizontal motion of water, range d=vt ⇒d=8 m [from (1) and (2)] Hence, horizontal range of water stream on the ground is d=8 m.

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