consider the point of intersection where the vertical line x=2 meets the line y=7x+1 what is the y-coordinate
1 answer:
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Answer:
The distance between them after 30 minutes is 6.5 km.
Step-by-step explanation:
Speed =
Sarah's speed = 6 km/hr = 1.6667 m/s
Emily's speed = 10 km/hr = 2.7778 m/s
The measure of angle between their bearings =
After 30 minutes (1800 seconds);
distance = speed x time
Sarah would have covered a distance = 1.6667 x 1800
= 3000 m
= 3 km
Emily would have covered a distance = 2.7778 x 1800
= 5000 m
= 5 km
The distance between them, a, can be determined by applying the cosine rule;
=
+
- 2bcCos A
= +
-2(5000 x 3000) Cos 105
= +
-2(5000 x 3000) x (-0.2588)
= 2.5 x + 9 x
+ 7764000
= 41764000
a =
= 6462.5073
a = 6462.5 m
The distance between them after 30 minutes is 6.5 km.
Although the formula looks involved, the key here is looking to see where the information goes.
We are given all the pieces but need to convert mph to ft/s to use the formula. Let's do it with 1 mph so that we have a ratio to use. We and solve a unit conversion problem.
That ratio tells us that 1 mph is 1.466666 ft/s. Now we solve two proportions.
1 mph / 1.466666 feet per second = 60 mph / x feet per second.
1x = (60)(1.466666)
So x = 88 feet per second.
Next, We repeat for 24 mph.
1 mph / 1.46666 feet per second = 24 mph / x feet per second.
1x = (1.4666666)(24)
x = 35.2 feet per second
Now we have the found appropriate V₁ and V₂. V₁ > V₂, so V₁ is 88 ft/s and V₂ is 35.2 ft/s. The problem tells us θ = 2.3 degrees, K₁ = .4 and K₂ = .06. The rest of the problem is calculator work. Start by substituting our degree measure of 2.3 degrees and the given values in the problem for V₁, V₂, K₁, and K₂
D = 6830.208 / 32.208372
D = 212.0631 = 212 (to the nearest foot)
Thus the car needs 212 feet to stop.