Page 75 - Calc for the Clueless

1.4
4
1.4
PV = k. Differentiating with respect to time, we get P(1.4V. dV/dt) + V dP/dt = 0. It looks messy at this
point, but fear not.

Substituting, we get

Example 22—

At 7 a.m. a plane flies over the city going east at 600 mph. At 9 a.m. a plane flies over the city going north at
350 mph. At what rate were the planes separating at 11 a.m.?

The key is to first make a drawing at the middle time, 9 a.m. The first plane is going east at 600 mph × 2 hours
= 1200 miles east of the city and keeps on going east. The distance is 1200 + x. At 9 a.m., the other plane is
over the city and is going north, distance 0 + y = y. Let z be the distance between the planes.

Find d/dt.

The separating speed

dx/dt = 600; 9 a.m. to 11 a.m. = 2 hours × 600 = 1200 = x.

dy/dt = 350; time = 2 hours × 350 = 700 = y.

Sticking numbers in the 11 a.m. picture and using old Pythagorus, we get z = 2500 (7,24,25 right triangle).