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We are given two equations representing the altitudes of two parachutists. 

1. **First parachutist**'s altitude equation:  
   \[
   y = -4t + 300
   \]
   where \( t \) is time in seconds after the first parachutist jumps.

2. **Second parachutist**'s altitude equation:  
   \[
   y = -4.9(t - 5)^2 + 300
   \]
   where \( t \) is the same time scale, but the second parachutist jumps 5 seconds later.

### Task: 
We need to find the time \( t \) when the second parachutist reaches the same altitude as the first parachutist.

### Solution:
Set the two equations equal to each other, since we are looking for the time when their altitudes are equal:
\[
-4t + 300 = -4.9(t - 5)^2 + 300
\]

The constants \( +300 \) on both sides cancel out, simplifying to:
\[
-4t = -4.9(t - 5)^2
\]

Next, I'll solve for \( t \). Let's start by expanding the quadratic on the right-hand side.The second parachutist reaches the same altitude as the first parachutist at two different times:

- \( t \approx 3.35 \) seconds
- \( t \approx 7.47 \) seconds

Since the second parachutist jumps 5 seconds later, we can discard the first solution (since it represents a time before the second parachutist jumps). Thus, the valid solution is:

\[
t \approx 7.47 \text{ seconds}
\]

This means the second parachutist reaches the same altitude as the first parachutist approximately 7.47 seconds after the first parachutist jumps.

Do you have any questions, or would you like further details?

Here are five related questions to explore:
1. How does the initial delay between the parachutists affect their meeting time?
2. What would happen to the equations if the second parachutist delayed her jump by 10 seconds instead of 5?
3. How can we model the altitude if the parachutist accelerates during free fall?
4. What is the rate of descent for each parachutist at the time they meet?
5. How could this problem be extended to model air resistance?

**Tip**: For problems involving free fall, using quadratic models allows for more accurate descriptions of the effects of gravity on motion.

A parachutist jumps from an airplane and immediately opens his parachute. His altitude, y, in metres, after t seconds is modelled by the equation y = -4t + 300. A second parachutist jumps 5 s later and freefalls for a few seconds. Her altitude, in metres, during this time, is modelled by the equation y = -4.9(t - 5)^2 + 300. When does she reach the same altitude as the first parachutist?

This problem involves solving for the time when two parachutists, with different altitude equations, reach the same altitude. Learn how to solve quadratic and linear equations and apply the quadratic formula. Suitable for high school students in Grades 9-11.

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