Suppose that a hot air balloon moving due east at a speed of 15 mile per hour (mph) and at a constant

altitude of 100 feet passes directly overhead. Thirty seconds later, what is the distance between me and
the balloon?

30 seconds = 30/3600 = 1/120 hour

in 1/120 hr, balloon has gone 15/120 = 1/8 mi = 660 ft

Now you have a right triangle, with legs 100 and 660

d^2 = 100^2 + 660^2 = 445600
d = 667.5 ft

To find the distance between you and the balloon, we need to consider the relative motion of both objects.

Given that the hot air balloon is moving due east at a constant speed of 15 mph, and assuming that you are stationary, we can calculate the distance using the formula:

Distance = Speed × Time

In this case, we need to find the distance covered by the hot air balloon in 30 seconds, while it is moving at a speed of 15 mph.

First, we need to convert 15 mph into feet per second, as the altitude is given in feet. There are 5280 feet in a mile, and 3600 seconds in an hour. So, to convert mph to feet per second, we can use the following two conversion factors:

1 mph = 5280 feet / 3600 seconds
15 mph = (15 * 5280) / 3600 feet / second

Now, we can calculate the distance covered by the hot air balloon in 30 seconds using the formula mentioned earlier:

Distance = (Speed of the balloon × Time) + Altitude

Distance = [(15 * 5280) / 3600 feet/second × 30 seconds] + 100 feet

Simplifying the equation:

Distance = (79200 / 3600 feet/second × 30 seconds) + 100 feet

Distance = 660 feet + 100 feet

Distance = 760 feet

Therefore, the distance between you and the balloon, after 30 seconds, is 760 feet.