A top-gun pilot, practicing radar avoidance maneuvers, is flying horizontally at 1300 km/hr, just 35 m above level ground. Suddenly, the plane encounters terrain that slopes gently upwards at 5, an amount difficult to detect visually. If the pilot doesn’t correct his trajectory, calculate the time the pilot has before flying into the ground?
distance to intercept=.035km ctn 5
time: distance/speed=.035ctn5/(1300km/hr)
convert that time to minutes
To calculate the time the pilot has before flying into the ground, we need to find the distance the plane will cover vertically and divide it by the vertical velocity of the plane.
First, let's find the distance the plane will cover vertically. We can use trigonometry to calculate this.
Given:
- The slope of the terrain is 5 degrees.
- The height of the plane above the ground is 35 m.
Using trigonometry, we can determine that the vertical distance the plane will cover can be calculated as follows:
Vertical distance = height of the plane * tan(slope angle)
Vertical distance = 35 m * tan(5 degrees)
Now, let's calculate the vertical distance.
Vertical distance = 35 m * tan(5 degrees)
Vertical distance ≈ 3.67 m
So, the plane will cover approximately 3.67 meters vertically.
Next, let's calculate the time it will take for the plane to cover this vertical distance.
Given:
- The plane is flying horizontally at 1300 km/hr.
To convert from kilometers per hour to meters per second, we need to divide by 3.6 (since there are 1000 meters in a kilometer and 3600 seconds in an hour).
Speed of the plane = 1300 km/hr ÷ 3.6 = 361.11 m/s (rounded to two decimal places)
Now, we can calculate the time it will take the plane to cover the vertical distance.
Time = Vertical distance ÷ Speed of the plane
Time = 3.67 m ÷ 361.11 m/s
Time ≈ 0.01 seconds
Therefore, the pilot has approximately 0.01 seconds before flying into the ground if they don't correct their trajectory.