A robot fires a tennis ball to protect itself from an incoming baseball. The trajectory of the tennis ball shot from the robot is given by r(s)=⟨10−20s,103–√−203–√s,15s−5s2⟩, where r(0) is the position of the robot, and the baseball has a trajectory given by b(t)=⟨5t,53–√t,10t−5t2⟩, t≥0. At what time t0 should the robot fire the tennis ball so that it collides with the baseball?

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.