When an airplane leaves the runway, its angle of ascent is 13° with a speed of 82 metres per second. Find the altitude of the plane after 7 minutes.
h/(82*7*60) = sin 13°
To find the altitude of the plane after 7 minutes, we first need to calculate the horizontal distance the plane would have traveled in 7 minutes.
The speed of the plane is given as 82 meters per second. Therefore, in 1 minute (60 seconds), the plane would have traveled a distance of:
Distance = Speed × Time
Distance = 82 m/s × 60 s = 4920 meters
Now, we can use trigonometry to find the vertical component of the distance the plane travels.
Since the angle of ascent is given as 13°, the vertical component of the distance traveled is found using the formula:
Vertical Distance = Horizontal Distance × tan(angle)
Vertical Distance = 4920 meters × tan(13°)
Using a calculator to approximate the value of tan(13°), we get:
Vertical Distance ≈ 4920 meters × 0.2287 ≈ 1125.84 meters
Therefore, the altitude of the plane after 7 minutes is approximately 1125.84 meters.