Part C In aviation, it is helpful for pilots to know the cloud ceiling, which is

Question

Part C

In aviation, it is helpful for pilots to know the cloud ceiling, which is the distance between the ground and lowest cloud. The simplest way to measure this is by using a spotlight to shine a beam of light up at the clouds and measuring the angle between the ground and where the beam hits the clouds. If the spotlight on the ground is 0.75 km from the hangar door as shown in (Figure 3), what is the cloud ceiling?

Part D

A person is rowing across the river with a velocity of 4.5 km/hr northward. The river is flowing eastward at 3.5 km/hr (Figure 4). What is the magnitude of her velocity (v) with respect to the shore?

Explanation / Answer

part C)

for the height h

tan(20 degree) = h/distance

tan(20 degree) = h/0.75

h = 0.273 km

the cloud ceiling is 0.273 km

part D)

for the magnitude of velcity wrt shore

magnitude of velcity wrt shore = sqrt(v^2 + u^2)

magnitude of velcity wrt shore = sqrt(4.5^2 + 3.5^2)

magnitude of velcity wrt shore 5.7 km/hr

the magnitude of velcity wrt shore is 5.7 km/hr

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