an airplane is flying at a constant altitude of 28000 meters. when first seen to the east of the observer, the angle to the airplane is 71.5 degrees. after 73 seconds, the angle of elevation is 51.6 degrees. find the speed of the airplane.
draw two triangles, one that has an angle of 71.5º and another with an angle of 51.6º
lets find the base in each one, call the first one x, the other one y
tan71.5 = 28000/x
x = 28000/tan71.5 = 9368.67
tan51.6 = 2800/y
y = 22192.53
So the horizontal distance travelled in 73 seconds is y-x = 12823.86
speed = distance/time = 12823.86/73
= 128.34 m/second
BTW, that airplane must be a spacecraft to fly at a height of 28 km, lol
I need help with Fraction vocabulary worksheet
If that is the case, then this should be a new question and thus a new topic.
To find the speed of the airplane, we need to use trigonometry and the concept of average speed. Here's how we can approach the problem step by step:
Step 1: Draw a diagram:
- Draw a right triangle, where the horizontal line represents the ground, the vertical line represents the altitude of the airplane (28000 meters), and the hypotenuse represents the distance between the observer and the airplane.
- Label the angle when first seen as 71.5 degrees and the angle after 73 seconds as 51.6 degrees.
- The side opposite to the angle of elevation (51.6 degrees) will be the difference in altitude traveled by the airplane in 73 seconds.
Step 2: Find the altitude difference:
- We know that the altitude difference is equal to the difference between 28000 meters and the altitude when the airplane was first seen.
- Since the altitude remains the same (constant), the altitude difference is the same as the side opposite to the angle of elevation.
Step 3: Find the horizontal distance traveled by the airplane:
- We can use the tangent function to find the ratio of the opposite (altitude difference) to the adjacent (horizontal distance).
- Using the angle of elevation (51.6 degrees), the tangent is given by: tan(51.6) = altitude difference / x (horizontal distance).
Step 4: Find the time taken to travel the horizontal distance:
- To find the time taken to travel the horizontal distance, we divide the horizontal distance (x) by the speed of the airplane.
- We can represent this as: x = speed * time.
Step 5: Use the time and altitude difference to find the speed:
- Since the time taken to travel the horizontal distance is 73 seconds and the altitude difference is the same as the side opposite to the angle of elevation (found in step 2), we can use the equation from step 4 to find the speed.
In summary, to find the speed of the airplane, we need to use the tangent function to find the horizontal distance traveled, which will be equal to the speed multiplied by the time taken to travel that distance. By rearranging the equations, we can solve for the speed.