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nataly862011
1 month ago
12

A fire hose held near the ground shoots water at a speed of 6.5 m/s. At what angle(s) should the nozzle point in order that the

water land 2.5m away?
Physics
1 answer:
inna [3.1K]1 month ago
8 0
The velocity of water can be decomposed into its vertical and horizontal components:
v_x = 6.5 cos \theta \\ v_y = 6.5 sin \theta

The vertical component will exhibit a parabolic trajectory due to gravity, while the horizontal component will be linear:
y(t) = -4.9t^2 + (6.5sin \theta) t \\ \\ x(t) = (6.5 cos \theta) t
To determine when the water reaches the ground 2.5m away, set y= 0 and x = 2.5
-4.9t^2 + (6.5sin \theta) t=0 \\ \\ t = \frac{6.5}{4.9} sin \theta \\ \\(6.5 cos \theta)(\frac{6.5}{4.9} sin \theta) = 2.5 \\ \\ sin \theta cos \theta = 0.29 \\ \\ sin 2\theta = 0.58 \\ \\ 2\theta = 35.4, 144.6 \\ \\ \theta = 17.7,72.3
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