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