Two planes approach each other head-on. Each has a speed of 780 km/hour,and they spot each other when they are 10.0 km apart. How much time do the pilots have to take evasive action?
their combined speed is 1560 km/hr
time = distance/speed, so ...
To find out the time the pilots have to take evasive action, we need to calculate the time it takes for the two planes to meet.
Let's first convert the speed from km/h to km/min so that the unit of time used is consistent.
1 hour = 60 minutes
Therefore, the speed of each plane can be expressed as:
780 km/hour = 780 km / 60 minutes
Now we can find the time it takes for the planes to meet:
The relative speed at which the planes are approaching each other is the sum of their speeds:
Relative speed = 780 km/60 minutes + 780 km/60 minutes
= (780 + 780) km/60 minutes
= 1560 km/60 minutes
= 26 km/minute
To find the time taken to meet, we divide the distance between the planes by the relative speed:
Time taken = Distance / Relative speed
= 10 km / 26 km/minute
To simplify the division, we can multiply the numerator and denominator by the reciprocal of the relative speed:
Time taken = 10 km * (1/(26 km/minute))
= 10 km * (1 minute/26 km)
= (10/26) minute
Let's simplify the fraction:
Time taken = 0.3846 minute
Therefore, the pilots have approximately 0.3846 minute or 23.08 seconds to take evasive action.
To find out the time the pilots have to take evasive action, we can use the formula:
time = distance / speed
First, let's determine the relative speed at which the two planes are approaching each other. Since they are approaching head-on, we can add their speeds together:
relative speed = plane speed + plane speed
relative speed = 780 km/h + 780 km/h
relative speed = 1560 km/h
Now, we can use the formula to calculate the time:
time = distance / relative speed
time = 10.0 km / 1560 km/h
time ≈ 0.0064 hours
To convert this time to minutes, we can multiply it by 60:
time ≈ 0.0064 hours * 60 minutes/hour
time ≈ 0.384 minutes
Therefore, the pilots have approximately 0.384 minutes (or about 23 seconds) to take evasive action.