After leaving the runway, a plane's angle of ascent is 16° and its speed is 267 feet per second. How many minutes will it take for the airplane to climb to a height of 12,500 feet? Round answer to two decimal places.
I know the answer is 2.83, but how?
if it's air speed is 267 ft/s, then its vertical speed is
267 sin 16° = 73.595 ft/s
So, to gain an altitude of 12500 ft takes
12500/73.595 = 169.848 seconds, or 2.83 minutes
Why did the plane become a mathematician?
Because it wanted to soar to new heights with its angles and numbers!
Now, let's solve this puzzle together. To find out how long it will take for the plane to climb to a height of 12,500 feet, we need to first determine the vertical component of the plane's speed.
By using some trigonometry magic, we can calculate that the vertical component of the speed is 267 * sin(16°).
Once we have the vertical speed, we can divide the height of 12,500 feet by the vertical speed to find the time it will take in seconds.
Finally, we can convert the time from seconds to minutes by dividing by 60.
So, in short, the answer is 2.83 minutes or approximately 2 minutes and 50 seconds.
Now, let's not keep that plane waiting any longer! It's time to take off to mathematical greatness!
To calculate the time it takes for the airplane to climb to a certain height, you can use the concept of trigonometry and basic physics.
First, let's break down the information given:
Angle of ascent (θ): 16°
Speed of the airplane (v): 267 feet per second
Height to climb (h): 12,500 feet
From the given information, we can determine the vertical component of the airplane's velocity. Using trigonometry, we can find that the vertical component (v_vertical) is calculated by multiplying the speed (v) by the sine of the angle of ascent (θ):
v_vertical = v * sin(θ) = 267 * sin(16°)
Next, we can determine the time it takes for the airplane to climb by dividing the height to climb (h) by the vertical component of velocity (v_vertical):
time = h / v_vertical
Substituting the values, we get:
time = 12,500 / (267 * sin(16°))
Evaluating this expression using a calculator, the answer is approximately 2.83 minutes, rounded to two decimal places.
To determine the time it takes for the airplane to climb to a height of 12,500 feet, we can use trigonometry and the given information about the plane's angle of ascent and speed.
First, we can break down the plane's speed into vertical and horizontal components. The vertical component of the speed is given by:
Vertical speed = Speed * sin(angle of ascent)
= 267 ft/s * sin(16°)
Next, we can determine the time it takes for the plane to climb to the desired height of 12,500 feet using the formula:
Time = Height / Vertical speed
= 12,500 ft / (267 ft/s * sin(16°))
Now, let's calculate the values:
Vertical speed ≈ 267 ft/s * 0.276 * (rounded value of sin(16°) to three decimal places)
Vertical speed ≈ 73.692 ft/s (rounded to three decimal places)
Time ≈ 12,500 ft / 73.692 ft/s
Time ≈ 169.618 seconds
Since we need the answer in minutes, we divide the time in seconds by 60:
Time ≈ 169.618 seconds / 60
Time ≈ 2.827 minutes (rounded to two decimal places)
Therefore, it will take approximately 2.83 minutes for the airplane to climb to a height of 12,500 feet.