# Tutor profile: Katherine P.

## Questions

### Subject: Physics (Newtonian Mechanics)

A ball is dropped gently from the top of the tower and another ball is thrown horizontally from the same point at the same time. Which ball will hit the ground earlier?

Ignoring the air resistance, assuming uniform gravity , small velocity of throwing and flat ground, both hit the ground at the same time. There is no acceleration in the horizontal direction, only vertical due to gravity!

### Subject: Pre-Calculus

How long is the hypotenuse of a right triangle with one side measuring 4cm and another measuring 6cm?

Using pythagoras' theorem, the sum of the two smaller squares is equal to the square of the hypotenuse. Therefore, its length is √52 = 7.21cm.

### Subject: Calculus

What is a derivative?

The derivative measures the steepness of the graph of a function at a particular point, also known as the slope. If the independent variable happens to be time, we often think of the derivative as a rate of change (an example is velocity). Formally, the derivative of function f at x=c is the limit of the slope of the secant line from x=c to x=c+h as h approaches 0.

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