An anti-aircraft shell is fired vertically upward with a muzzle velocity of 488m/s. Determine:

a. the maximum height it can reach



To determine the maximum height that the anti-aircraft shell can reach, we can use the kinematic equations for uniformly accelerated motion. When the shell is fired vertically upward, it will decelerate due to gravity until its velocity becomes zero at the maximum height.

Given:
- Initial velocity (\(v_0\)) = 488 m/s
- Acceleration due to gravity (\(g\)) = 9.8 m/s² (downward)

At the maximum height, the final velocity (\(v\)) will be 0 m/s.

We use the following kinematic equation to find the maximum height (\(h_{max}\)):

\[ v^2 = v_0^2 + 2a s \]

Where:
- \(v\) is the final velocity (0 m/s at the maximum height)
- \(v_0\) is the initial velocity (488 m/s)
- \(a\) is the acceleration (-9.8 m/s², since gravity acts downward)
- \(s\) is the displacement (maximum height, \(h_{max}\))

Rearranging the equation to solve for \(s\):

\[ 0 = (488 \, \text{m/s})^2 + 2(-9.8 \, \text{m/s}^2) s \]

\[ 0 = 238144 - 19.6s \]

\[ 19.6s = 238144 \]

\[ s = \frac{238144}{19.6} \]

\[ s = 12155.1 \, \text{m} \]

Therefore, the maximum height (\(h_{max}\)) the shell can reach is 12155.1 meters.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. What would be the time taken to reach the maximum height?
2. How long will it take for the shell to return to the ground?
3. What would be the total time of flight for the shell?
4. How would air resistance affect the maximum height reached by the shell?
5. What would be the impact velocity of the shell when it hits the ground?

**Tip:** When dealing with projectile motion, breaking the problem into vertical and horizontal components simplifies the calculations.

Learn how to calculate the maximum height reached by an anti-aircraft shell fired vertically upward with a muzzle velocity of 488 m/s. This problem involves using kinematic equations for uniformly accelerated motion, specifically the equation relating initial velocity, acceleration due to gravity, and displacement.

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