The boat in Figure below is heading due north as it crosses a wide river with a

Question

The boat in Figure below is heading due north as it crosses a wide river with a velocity of 10.0 m/s relative to the water. The river has a uniform velocity of 2.50 m/s due east. (a) Determine the far respect to an observer on the riverbank.(b) the river is 200 m wide, how downstream has boat moved by the time it reaches the north shore? A fireman unknown distance away from a burning building directs a steam of water from a ground-level fire hose at an angle of 35 degree above the horizontal. If the speed of water steam as it leaves the hose is 40 m/s, and the stream of water strike the building at the height of 20.0 meter, what is unknown distance the fireman away from the building?

Explanation / Answer

(a)

velocity of boat relative to observer on ground Vbg = Vbw + VwG

Vbg = 10j + 2.5 i

magnitude = sqrt(10^2+2.5^2) = 10.3 m/s <<<----answer

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(b)

from the figure

vwG/VbW = x/200

x = (2.5/10)*200 = 50 m   <<<<<----answer

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PROJECTILE

1)

along horizantal

initial velocity vox = vo*costheta

ax = 0

from equaiton of motion

x = vox*T+ 0.5*ax*T^2

x = vo*costheta*T

T = x/(vo*costheta)......(1)

along vertical

voy = vo*sintheta

acceleration ay = -g = -9.8 m/s^2

from equation of motion

y = voy*T + 0.5*ay*T^2

y = (vo*sintheta*x)/(vo*costhetra) - (0.5*g*x^2)/(vo^2*(costheta)^2)

y = x*tantheta - ((0.5*g*x^2)/(vo^2*(costheta)^2))

20 = (x*tan35) - (0.5*9.8*x^2/(40^2*(cos35)^2))

x = 115.4 m <<<<<----------answer

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