An artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. To clear an...

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16. An artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. To clear an avalanche, it explodes on a mountainside 42.0 s after firing. What are the x- and y-coordinates of the shell where it explodes, relative to its firing point?
18. A fireman d = 50.0 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of θ_i = 30.0° above the horizontal as shown in Figure P3.18. If the speed of the stream as it leaves the hose is v_i = 40.0 m/s, at what height will the stream of water strike the building?

SnapAndSolve AI · Accepted Answer

To find the x- and y-coordinates of the shell where it explodes, we use the following equations of motion:

x-coordinate:
x = v_i * cos(θ) * t
x = 300 m/s * cos(55.0°) * 42.0 s
x ≈ 7230.5 m

y-coordinate:
y = v_i * sin(θ) * t - 0.5 * g * t^2
y = 300 m/s * sin(55.0°) * 42.0 s - 0.5 * 9.8 m/s² * (42.0 s)^2
y ≈ 4622.4 m
To find the height at which the stream of water strikes the building, we use the following equations:

Time to reach the building:
t = d / (v_i * cos(θ_i))
t = 50.0 m / (40.0 m/s * cos(30.0°))
t ≈ 1.44 s

Height:
h = v_i * sin(θ_i) * t - 0.5 * g * t^2
h = 40.0 m/s * sin(30.0°) * 1.44 s - 0.5 * 9.8 m/s² * (1.44 s)^2
h ≈ 15.3 m

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An artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. To clear an...

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