18) A projectile is fired from point 0 at the edge of a cliff, with initial velocity components of vox 60.0 m/s and voy 175 m/s, as shown in the figure. The projectile rises and then falls into the sea at point P. The time of flight of the projectile is 40.0 s, and it experiences no appréciable air resistance in flight. What is the height of the cliff? 


To find the height of the cliff, we can focus on the vertical motion of the projectile. We know the following information:

- Initial vertical velocity: \( v_{0y} = 175 \, \text{m/s} \)
- Time of flight: \( t = 40.0 \, \text{s} \)
- Gravitational acceleration: \( g = 9.8 \, \text{m/s}^2 \)
- The projectile ends up at a point lower than its starting height (since it falls into the sea), which means the vertical displacement will give us the height of the cliff.

### Step 1: Equation for vertical displacement

The vertical displacement \( y \) after time \( t \) can be calculated using the kinematic equation:

\[
y = v_{0y} \cdot t - \frac{1}{2} g \cdot t^2
\]

where:
- \( v_{0y} = 175 \, \text{m/s} \)
- \( t = 40.0 \, \text{s} \)
- \( g = 9.8 \, \text{m/s}^2 \)

### Step 2: Calculate the vertical displacement

Now, let's plug in the values and calculate the displacement.

\[
y = (175 \, \text{m/s}) \cdot (40.0 \, \text{s}) - \frac{1}{2} (9.8 \, \text{m/s}^2) \cdot (40.0 \, \text{s})^2
\]

Let's calculate this:The vertical displacement \( y \) is approximately \(-840 \, \text{m}\). Since this displacement is negative, it indicates that the projectile ends up 840 meters below its starting point, meaning the height of the cliff is **840 meters**.

Would you like any additional details or further clarification?

Here are 5 related questions to expand on this topic:
1. What would be the maximum height reached by the projectile?
2. How would air resistance affect the projectile's motion?
3. Can we calculate the range (horizontal distance) of the projectile?
4. What would happen to the time of flight if the initial vertical velocity were doubled?
5. How does the angle of projection affect the flight of a projectile?

**Tip:** The horizontal and vertical motions of a projectile are independent of each other. Always treat them separately when solving projectile motion problems.

A projectile is fired from point 0 at the edge of a cliff, with initial velocity components of vox 60.0 m/s and voy 175 m/s, as shown in the figure. The projectile rises and then falls into the sea at point P. The time of flight of the projectile is 40.0 s, and it experiences no appreciable air resistance in flight. What is the height of the cliff?

Learn how to calculate the height of a cliff from which a projectile is fired, with initial velocity components of 60.0 m/s (horizontal) and 175 m/s (vertical). Using kinematic equations and the given time of flight of 40 seconds, we find that the height of the cliff is 840 meters. This problem explores key concepts of projectile motion and vertical displacement, ideal for Grades 11-12 physics students.

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