Sue is in an airplane which travels at a constant 300 kilometers per hour. The angle of climb of the airplane is 30
∘. How long (in seconds) would it take from takeoff,
before the airplane reaches 3000 meters, when Sue can access Wifi and work on the rest of the weekly problems?
the distance flown,
d = 3000/sin30° = 6000m
That's 6km, so it will take 6/300 = 1/50 hr = 72 seconds
To find the time it takes for the airplane to reach 3000 meters, we need to determine the distance Sue travels in that time.
First, let's convert the given altitude from meters to kilometers. We know that 1 kilometer is equal to 1000 meters, so 3000 meters is equal to 3000/1000 = 3 kilometers.
Next, we will calculate the time it takes to travel 3 kilometers at a constant speed of 300 kilometers per hour.
The formula to calculate the time is:
Time = Distance / Speed
In this case, the distance is 3 kilometers and the speed is 300 kilometers per hour.
Time = 3 km / 300 km/hr
To get the time in hours, we divide the distance by the speed:
Time = 3 / 300
Now, we need to convert this time from hours to seconds.
Since 1 hour is equal to 3600 seconds, we can convert the time from hours to seconds by multiplying by 3600:
Time = (3 / 300) * 3600
Simplifying the expression:
Time = 0.01 * 3600
Time = 36 seconds
Therefore, it would take Sue 36 seconds from takeoff before the airplane reaches an altitude of 3000 meters and she can access Wifi and work on the rest of the weekly problems.