A plane flies at a speed of 150mph at an angle of 10 degrees, after 6 seconds, the plane keeps the same speed but changes to an angle 18 degrees. How long in minutes would it take the plane to travel to a cruising altitude of 30,000 feet?
change mph to feet/sec
(60mph=88fps)
speed=150*88/60=...
30,000ft=speed*6*sin10+speed((t-6)*sin18
solve for time t. then, divide by 60 to get minutes
To solve this problem, we need to break it down into steps.
Step 1: Calculate the horizontal and vertical components of the velocity.
Let's start by calculating the horizontal and vertical components of the velocity for the initial angle of 10 degrees.
Given:
Speed of the plane = 150 mph
Angle = 10 degrees
Horizontal component of velocity = Speed * cos(angle)
Vertical component of velocity = Speed * sin(angle)
Horizontal component of velocity = 150 * cos(10)
Vertical component of velocity = 150 * sin(10)
Step 2: Calculate the time it takes for the plane to change its angle.
To calculate the time it takes for the plane to change its angle from 10 degrees to 18 degrees, we need to determine the change in angle.
Change in angle = Final angle - Initial angle
Change in angle = 18 - 10
Now, we need to calculate the time it takes for the plane to change its angle.
Given:
Angle change rate = 6 seconds
Time = Change in angle / Angle change rate
Time = (18 - 10) / 6
Step 3: Calculate the distance traveled during the angle change.
To calculate the distance traveled during the angle change, we need to calculate the horizontal and vertical distances separately.
Given:
Time during angle change = Result from Step 2
Vertical component of velocity = Result from Step 1
Vertical distance = Vertical component of velocity * Time during angle change
Horizontal distance = Horizontal component of velocity * Time during angle change
Step 4: Calculate the time it takes for the plane to reach a cruising altitude of 30,000 feet.
To calculate the time it takes for the plane to reach a cruising altitude of 30,000 feet, we need to determine the total distance traveled vertically.
Given:
Cruising altitude = 30,000 feet
Vertical distance during angle change = Result from Step 3
Total vertical distance = Cruising altitude - Vertical distance during angle change
Now, we need to calculate the time it takes for the plane to reach the cruising altitude.
Time = Total vertical distance / Vertical component of velocity
Step 5: Convert the time to minutes.
The result from Step 4 might be in seconds, so let's convert it to minutes.
Convert time from seconds to minutes:
Time in minutes = Time in seconds / 60
By following these steps, we can find the time it would take for the plane to travel to a cruising altitude of 30,000 feet.