# Question #8f27f

##### 1 Answer

The problem is as shown in the figure below. Momentarily both the bus and Sophia are still and are

1. Suppose Sophia catches the bus after time

Kinematic equation for Sophia

Distance ran

In this duration Bus moves

To catch the bus, distance run by Sophia

Rewriting we obtain

Multiplying both sides with

using the formula to find roots of a quadratic

Selecting

Distance run by Sophia in this time

2. There is no change in the kinematic equation for the bus. But for Sophia we have

Distance ran

To catch the bus, distance run by Sophia

Rewriting we obtain

Multiplying both sides with

Now this time

We see that discriminant is

3. Suppose Sophia needs to run at a velocity of

There is no change in the kinematic equation for the bus. But for Sophia we have

Distance ran

To catch the bus, distance run by Sophia

Rewriting we obtain

Multiplying both sides with

Using the formula for roots of a quadratic

For real roots and with minimum velocity required for Sophia to run the discriminant must be set to be

Solving for

Ignoring the