A small plane takes off from an airport and begins to climb at a 10 degree angle of elevation at 5000 ft/minute. After 3 minutes, how far along the ground will the plane have flown?
28356.4 ft
To find how far the plane will have flown, we need to find the horizontal component of its displacement.
Given that the plane is climbing at a 10-degree angle, we can use trigonometry to calculate the horizontal component of its displacement. The horizontal displacement is given by the equation:
Horizontal displacement = Vertical displacement * tan(angle)
In this case, the vertical displacement is the rate at which the plane is climbing, which is 5000 ft/minute, and the angle is 10 degrees.
Horizontal displacement = (5000 ft/minute) * tan(10 degrees)
To find the value of tan(10 degrees), we can use a scientific calculator or an online calculator. Entering "tan(10 degrees)" into the calculator, we get approximately 0.1763.
Horizontal displacement = (5000 ft/minute) * 0.1763
Multiplying these values together, we get:
Horizontal displacement ≈ 882.6 ft/minute
Since the plane has been flying for 3 minutes, we can find the total horizontal displacement by multiplying the horizontal displacement per minute by the number of minutes:
Total horizontal displacement = Horizontal displacement per minute * Number of minutes
Total horizontal displacement ≈ 882.6 ft/minute * 3 minutes
Calculating this, we get:
Total horizontal displacement ≈ 2647.8 ft
Therefore, after 3 minutes, the plane will have flown approximately 2647.8 feet along the ground.