A train goes up a hill with a 15º incline. If the train has constant speed of 22 m/s, what are the vertical and horizontal compo
nents of the train's velocity? (Remember to use the law of sine and cosines for this problem)
1 answer:
Sinθ=opposite side/hypotenuse
cosθ=adjacent side/hypotenuse
where both the sides are relative to theta.
in this case, 22 is your hypotenuse. theta (θ) is the angle you are examining. i've included a diagram for reference because the equations may format differently depending on which angle you choose as theta.
using my diagram:
sinθ = o/h
sin 15 = o/22
sin 15(22) = o
o=5.69m/s
therefore the vertical component is about 5.69m/s.
cosθ=a/h
cos15 = a/22
cos15(22) = a
a = 21.25m/s
therefore, your horizontal component is about 21.25m/s.
cosθ=adjacent side/hypotenuse
where both the sides are relative to theta.
in this case, 22 is your hypotenuse. theta (θ) is the angle you are examining. i've included a diagram for reference because the equations may format differently depending on which angle you choose as theta.
using my diagram:
sinθ = o/h
sin 15 = o/22
sin 15(22) = o
o=5.69m/s
therefore the vertical component is about 5.69m/s.
cosθ=a/h
cos15 = a/22
cos15(22) = a
a = 21.25m/s
therefore, your horizontal component is about 21.25m/s.
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Answer:
At the start of 2014, the population was growing at 8.34 million people per year.
At the start of 2015, the population was growing at 8.39 million people per year.
Step-by-step explanation:
To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.
The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).
We know that the population, P(t), of China, in billions, can be approximated by
To find the derivative you need to:
To find the population growing at the start of 2014 we say t = 0
To find the population growing at the start of 2015 we say t = 1
To convert billion to million you multiple by 1000