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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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