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Answer :
Answer:
The time taken for the airplane to climb to a height of 12,500 feet is 2.83 minutes.
Explanation:
Given that,
Angle of the plane of ascent, [tex]\theta=16^{\circ}[/tex]
Initial speed of the plane, u = 267 ft/s
We need to find the time taken for the airplane to climb to a height of 12,500 feet. First lets find the vertical speed of the plane.
[tex]u_y=u\ \sin\theta\\\\u_y=267\times \ \sin(16)\\\\u_y=73.59\ ft/s[/tex]
Let t is the time taken for the airplane to climb to a height of 12,500 feet. The speed of an object is given by :
[tex]u=\dfrac{d}{t}\\\\t=\dfrac{d}{u}\\\\t=\dfrac{12500\ ft}{73.59\ ft/s}\\\\t=169.86\ seconds\\\\t=2.83\ min[/tex]
So, the time taken for the airplane to climb to a height of 12,500 feet is 2.83 minutes. Hence, this is the required solution.
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Final answer:
By using sine to find the vertical component of the airplane's speed and then dividing the desired height by this vertical speed, we can find the time it takes for the airplane to reach 12,500 feet in altitude and then convert that time from seconds to minutes.
Explanation:
To calculate the time it takes for an airplane to climb to a height of 12,500 feet with an angle of ascent of 16 degrees and a speed of 267 feet per second, we need to apply trigonometry. Specifically, we will use the sine function to find the vertical component of the airplane's velocity.
The vertical component of the speed (Vv) can be calculated using the formula Vv = V * sin(θ), where V is the speed of the airplane and θ is the angle of ascent. Substituting the given values, we have Vv = 267 feet/sec * sin(16°).
Once we have the vertical component of the speed, we can find the time (t) to reach 12,500 feet using the formula t = distance / speed. The distance in this case is the height of 12,500 feet.
After calculating the time in seconds, we can convert it to minutes by dividing by 60, since there are 60 seconds in a minute.
