The problem can be solved using the given formula:

$S = V_i t + \frac{1}{2} g t^2$

Here:

• $S$ is the distance traveled (260,000 ft),
• $V_i$ is the initial velocity (starting from rest, so $V_i = 0$),
• $g$ is the acceleration (given as 60 km/s²),
• $t$ is the time of travel, which is currently unknown.

First, we'll convert the distance from feet to kilometers and use the acceleration in km/s². Then, we can solve for $t$, and once we have $t$, we can find the velocity.

Step 1: Convert 260,000 ft to kilometers

1 km = 3280.84 ft, so: $260,000 \, \text{ft} = \frac{260,000}{3280.84} \, \text{km} \approx 79.25 \, \text{km}$

Step 2: Apply the formula to solve for time $t$

Using $S = \frac{1}{2} g t^2$, since $V_i = 0$: $79.25 = \frac{1}{2} \times 60 \times t^2$

Now solve for $t$: $t^2 = \frac{79.25 \times 2}{60} = \frac{158.5}{60} \approx 2.642$ $t = \sqrt{2.642} \approx 1.625 \, \text{seconds}$

Step 3: Solve for the final velocity

The final velocity can be found using the formula: $V_f = V_i + g t$ Since $V_i = 0$, we have: $V_f = 60 \times 1.625 = 97.5 \, \text{km/s}$

Thus, the velocity of the supersonic jet after it travels 260,000 feet is approximately 97.5 km/s.

Would you like further clarification or details on any part of the solution?

Here are 5 related questions:

1. What would the velocity be if the acceleration was 80 km/s² instead?
2. How would the time change if the distance was doubled?
3. What would the total distance be if the jet traveled for 5 seconds?
4. Can we determine the energy required for this acceleration?
5. How would the velocity change if the jet started with an initial velocity?

Tip: Always check the units of each term before solving the equation to avoid errors in calculations.