Uniform Motion Related Problem
Two planes leave an airport at 2 p.m., one flying south at 450 kph, the other flying north at 675 kph. At what time will they be 3 600 apart?
1. -450 km/h(South).
2. 675 km/h(North).
675T - (-450T) = 3600 km.
Solve for T.
To solve this uniform motion problem, we need to determine the time it takes for the two planes to be 3,600 kilometers apart.
Let's consider the motion of the two planes. One plane is flying south at a speed of 450 kilometers per hour, while the other plane is flying north at a speed of 675 kilometers per hour. Since they are moving in opposite directions, their relative speed will be the sum of their individual speeds. Therefore, the relative speed of the two planes is 450 + 675 = 1,125 kilometers per hour.
To find the time it takes for the planes to be 3,600 kilometers apart, we can use the formula:
distance = speed × time
In this case, the distance is 3,600 kilometers and the relative speed is 1,125 kilometers per hour. Let's substitute these values into the formula:
3,600 = 1,125 × time
Now we can solve for time:
time = 3,600 / 1,125
Calculating this, we find that:
time ≈ 3.2 hours
Since the planes left the airport at 2 p.m., we can add 3.2 hours to find the time at which they will be 3,600 kilometers apart:
2 p.m. + 3.2 hours = 5:12 p.m.
Therefore, the planes will be 3,600 kilometers apart at approximately 5:12 p.m.