An aeroplane flies for 12minutes at a velocity of 430km/h due North
A) Calculate the displacement of the aeroplane
B) how long would the pilot take for the same flight if the average velocity of the aeroplane is increased by 20%?
A) To calculate the displacement of the aeroplane, we need to determine how far it has traveled in a straight line from its starting point. Since the velocity is due North, the displacement will only have a northward component.
First, we need to convert the flight time from minutes to hours:
12 minutes = 12/60 = 0.2 hours
Next, we use the formula:
Displacement = Velocity x Time
Given that the velocity is 430 km/h and the flight time is 0.2 hours, we can plug in the values to calculate the displacement:
Displacement = 430 km/h x 0.2 h = 86 km North
Therefore, the displacement of the aeroplane is 86 km North.
B) If the average velocity of the aeroplane is increased by 20%, we need to calculate the new velocity and the time it would take for the same flight.
To find the new velocity, we multiply the original velocity by 1 + 20% (which is the same as multiplying by 1.2):
New velocity = 430 km/h x 1.2 = 516 km/h
Now, we can calculate the new time using the formula:
Time = Displacement / Velocity
Given that the displacement is still 86 km North and the new velocity is 516 km/h, we can plug in the values to calculate the new time:
Time = 86 km / 516 km/h ≈ 0.167 hours
To convert the time from hours to minutes, we multiply by 60:
0.167 hours x 60 minutes/hour ≈ 10.02 minutes
Therefore, the pilot would take approximately 10 minutes and 1 second for the same flight if the average velocity of the aeroplane is increased by 20%.
or, for part B, if the velocity increases by 20%, then the time is decreased by a similar factor:
12 min / 1.20 = 10 minutes
Note that your answer is somewhat off:
Time = 86 km / 516 km/h = 1/6 hour = 10 minutes