Another rock in Death Valley at the Racetrack traveled 55.3 meters during the observation period of nine years. a . What was the rock's average speed in feet per year? Round your answer to the nearest whole number. feet per year b . If a strong wind gives a stone an initial velocity of v 0 = 11 m / s , and the friction coefficient of stone on ice is μ = 0.14 , and g = 9.81 m / s 2 . Use the equation v 2 0 = 2 μ g S to find the stopping distance S for the stone. Round your answer to the nearest tenth.
Answers
Answer:
a) 20 feet per year
b) 44.1 m
Step-by-step explanation:
Given:
Distance traveled during the observation period = 55.3 meters
Observation period = 9 years
initial velocity of v₀ = 11 m/s
friction coefficient of stone on ice is μ = 0.14
g = 9.81 m/s²
also,
v₀² = 2μgS
Now,
1 m = 3.28084 ft
thus,
Total distance in feet = 55.3 × 3.28084 = 181.430452 ft
Average speed =
or
Average speed =
or
Average speed = 20.159 feet/year ≈ 20 feet per year
b) v₀² = 2μgS
substituting the values in the above equation, we get
11² = 2 × 0.14 × 9.81 × s
or
121 = 2.7468 × s
or
s = 44.051 ≈ 44.1 m
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Step-by-step explanation:
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Answers
Final answer:
Cos(88°) can be estimated using the 3rd degree Taylor polynomial for cos(x) centered at a = π/2. The degrees need to be converted to radians, and by substituting into the polynomial, the cosine value to five decimal places is approximately 0.03490.
Explanation:
To estimate cos(88°) using the 3rd degree Taylor polynomial for cos(x) centered at a = π/2, we first need to convert 88 degrees to radians as cos(x) expects x in radians. 88 degrees is roughly 1.53589 radians. Now, substituting x = 1.53589 into the Taylor polynomial yields the estimate.
The given Taylor polynomial is represented as cos(x) = - (x - π/2) + 1/6 * (x - π/2)³. Substituting x with 1.53589, we get:
cos(1.53589) = - (1.53589 - π/2) + 1/6 * (1.53589 - π/2)³
To get the estimate correct to five decimal places, you calculate the above expression to get roughly 0.03490. Therefore, cos(88°) is approximately 0.03490.
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Final answer:
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This problem deals with the concept of Taylor series approximation, which is a widely used method in mathematics to estimate the value of functions. The given Taylor polynomial approximates the cosine function. To estimate cos(88°), we first need to convert the angle from degrees to radians, because the standard trigonometric functions in mathematics take input in radians. Remember that 180° equals π radians. So 88° can be represented as (88/180)π radians.
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