An Anti-aircraft shell is fired. vertically upward velocity of 488 m/s. Determine the time it takes to reach In this height

To determine the time it takes for the anti-aircraft shell to reach its maximum height, we can use the following kinematic equation:

\[
v_f = v_i + at
\]

Where:
- \( v_f \) is the final velocity at the maximum height (0 m/s, since it stops momentarily at the top),
- \( v_i \) is the initial velocity (488 m/s),
- \( a \) is the acceleration due to gravity (-9.8 m/s\(^2\)),
- \( t \) is the time it takes to reach the maximum height.

We can solve for \( t \) as follows:

\[
0 = 488 + (-9.8)t
\]

\[
9.8t = 488
\]

\[
t = \frac{488}{9.8} \approx 49.8 \text{ seconds}
\]

So, it takes approximately 49.8 seconds for the shell to reach its maximum height.

Would you like any more details or have any questions?

Here are 5 related questions to consider:
1. How can we calculate the maximum height the shell reaches?
2. What would be the total time of flight before the shell returns to the ground?
3. How would air resistance affect the time to reach the maximum height?
4. What is the velocity of the shell at different times during its ascent?
5. How much kinetic energy does the shell have at its maximum height?

**Tip:** In projectile motion problems, always define the direction of gravity as negative when using the upward direction as positive.

Learn how to calculate the time it takes for an anti-aircraft shell fired vertically with an initial velocity of 488 m/s to reach its maximum height. Includes step-by-step solution using kinematic equations. Suitable for high school students studying projectile motion.

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