Two ships are leaving port at the same time. The first ship is sailing due east at 20 km/hr and the other due north at 15 km/hr. How fast are the ships moving away from each other 2.0 hr later?
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To find the speed at which the ships are moving away from each other, we can use the Pythagorean theorem to find the distance between them after 2.0 hours, and then divide that distance by the time.
First, let's calculate the distance each ship has traveled after 2.0 hours.
The first ship is sailing due east at a speed of 20 km/hr, so in 2.0 hours, it will travel a distance of 20 km/hr * 2.0 hr = 40 km.
The second ship is sailing due north at a speed of 15 km/hr, so in 2.0 hours, it will travel a distance of 15 km/hr * 2.0 hr = 30 km.
Now, we can find the distance between the two ships after 2.0 hours using the Pythagorean theorem. The distance will be the hypotenuse of a right triangle, with the distances traveled by each ship as the legs.
Using the formula c^2 = a^2 + b^2, where c is the hypotenuse and a and b are the legs, we have:
c^2 = (40 km)^2 + (30 km)^2
c^2 = 1600 km^2 + 900 km^2
c^2 = 2500 km^2
Taking the square root of both sides, we get:
c = √(2500 km^2)
c = 50 km
So after 2.0 hours, the ships are 50 km apart.
To find the speed at which the ships are moving away from each other, we divide the distance of 50 km by the time of 2.0 hours:
speed = distance / time
speed = 50 km / 2.0 hr
speed = 25 km/hr
Therefore, the ships are moving away from each other at a speed of 25 km/hr after 2.0 hours.