Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A cheetah at chases a gazelle running at in a straight line. The cheetah can keep up that speed for only .
Along a line, the velocity of A relative to B is
Same direction: the difference of the speeds. Opposite directions: their sum.
In a chase, the gap closes at the relative velocity.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Closing speed. .
Step 2. A 60 m lead. , within the .
Step 3. A 100 m lead. In the cheetah gains , so the gazelle is still ahead.
Answer: (a) . (b) ahead: it escapes.
Check. The cheetah could catch any gazelle with a lead under .
Watch out. It is the relative speed, , not the cheetah's , that decides the chase.
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