Supersonic jet starting from rest accelerates at a constant rate of 60 km/s2. Solve for the velocity of the jet after it travels 260,000 ft. Formula: S=Vi+ gt

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.

Supersonic jet starting from rest accelerates at a constant rate of 60 km/s². Solve for the velocity of the jet after it travels 260,000 ft. Formula: S=Vi+ gt

Learn how to calculate the velocity of a supersonic jet starting from rest and accelerating at 60 km/s² after it travels 260,000 feet. This problem covers concepts of kinematics, constant acceleration, and unit conversion, suitable for Grades 10-12 students.

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