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.
Vo = 82m/s[13o].
Yo = 82*sin13 = 18.45 m/s.
h = Yo*t = 18.45m/s * 420s. = 7747 m.
To find the altitude of the plane after 7 minutes, we'll need to use the given information about the angle of ascent and speed.
First, let's convert the time from minutes to seconds. Since there are 60 seconds in a minute, 7 minutes is equal to 7 * 60 = 420 seconds.
To find the altitude, we can use trigonometric functions. The angle of ascent can be broken down into the vertical and horizontal components of the plane's motion.
The vertical component of the plane's motion can be found by multiplying the speed by the sine of the angle of ascent:
Vertical component = speed * sin(angle of ascent)
= 82 * sin(13°)
Now, let's calculate the vertical component of the plane's motion:
Vertical component = 82 * sin(13°)
≈ 82 * 0.227
≈ 18.634 meters per second
Next, we can find the altitude by multiplying the vertical component by the time:
Altitude = vertical component * time
= 18.634 * 420 meters
≈ 7815.48 meters
Therefore, the altitude of the plane after 7 minutes is approximately 7815.48 meters.