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

b. the time it takes to reach this height

To determine the time it takes for the anti-aircraft shell to reach its maximum height, we can use another kinematic equation for uniformly accelerated motion. 

Given:
- Initial velocity (\(v_0\)) = 488 m/s
- Final velocity (\(v\)) at maximum height = 0 m/s
- Acceleration due to gravity (\(g\)) = -9.8 m/s² (negative because it acts downward)

We use the following kinematic equation to find the time (\(t\)):

\[ v = v_0 + at \]

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

\[ t = \frac{v - v_0}{a} \]

Plugging in the values:

\[ t = \frac{0 \, \text{m/s} - 488 \, \text{m/s}}{-9.8 \, \text{m/s}^2} \]

\[ t = \frac{-488 \, \text{m/s}}{-9.8 \, \text{m/s}^2} \]

\[ t = 49.8 \, \text{s} \]

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

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. What is the total time of flight for the shell if it is fired and returns to the same height?
2. How would the time to reach the maximum height change if the initial velocity were doubled?
3. What is the maximum height if the initial velocity is 300 m/s instead of 488 m/s?
4. How does the angle of launch affect the time to reach maximum height in projectile motion?
5. How does the presence of air resistance alter the time to reach maximum height?

**Tip:** Understanding the symmetry of projectile motion can help solve problems more efficiently, especially when dealing with vertical motion.

Learn how to calculate the time it takes for an anti-aircraft shell fired vertically with a muzzle velocity of 488 m/s to reach its maximum height. Detailed step-by-step solution using kinematic equations for uniformly accelerated motion.

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