By Request: Entrance Exam Problem

Sameer Hemmady in Albuquerque writes:

A dog is chasing a cat with uniform velocity “v” so that at any given time the dog is “aimed” directly at the cat. The cat upon seeing the dog runs rectilinearly and uniformly with velocity “u” with u<v. At the initial moment when the cat sees the dog, the vectors v and u are perpendicular to each other, and the dog and cat are separated by a distance “d”. How soon will the dog catch up to the cat? (Problem in our engineering entrance exam in India)

Entrance exam problems require quite a bit of ingenuity to solve. This is something to be expected. They are not testing your ability to simply differentiate or integrate, but to create an approach to the problem. This ability is important if you plan to use calculus in your career (I actually solved a problem similar to this in my job, involving a jet and a ballistic interceptor). Math problems do not present themselves as equations for you to solve, but you must form the equations yourself from meaningful quantities in the word problem. Creating an approach to a problem takes quite a bit of trial and error. Therefore, when solving this problem I will consider different approaches.

Solving entrance exam problems is a science in its own right, and learning all there is about it would take several semester-long classes. However, even if you have never been exposed to entrance exam problems, and especially even if this is your first semester of calculus, I encourage you to look at the solution to the problem, and ask questions if you have any.

Click here for solution