A car drives off a 40m high cliff at a velocity of 34m/s. How far away from the bottom of the cliff does it land

To find out how far away from the bottom of the cliff the car lands, we can use the physics of projectile motion. We need to calculate the time it takes for the car to fall 40 meters and then use that time to find out how far it travels horizontally.

### Step 1: Calculate the time of fall

Using the formula for the vertical motion under gravity:

\[
h = \frac{1}{2} g t^2
\]

where:
- \( h = 40 \) m (height of the cliff)
- \( g = 9.81 \) m/s² (acceleration due to gravity)

Rearranging for \( t \):

\[
t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 40}{9.81}} \approx \sqrt{8.16} \approx 2.86 \text{ seconds}
\]

### Step 2: Calculate horizontal distance

The horizontal distance \( d \) can be calculated using the formula:

\[
d = v \cdot t
\]

where:
- \( v = 34 \) m/s (horizontal velocity)
- \( t \approx 2.86 \) s (time of fall)

Substituting the values:

\[
d = 34 \times 2.86 \approx 97.24 \text{ meters}
\]

### Conclusion

The car lands approximately **97.24 meters** away from the bottom of the cliff.

Would you like more details on any part of this solution? Here are some related questions you might consider:

1. What are the assumptions made in this calculation?
2. How would the result change if the initial velocity was different?
3. What would happen if air resistance was taken into account?
4. How can the motion be modeled graphically?
5. What other factors could influence the distance traveled by the car? 

**Tip:** Always consider both vertical and horizontal components in projectile motion problems!

A car drives off a 40m high cliff at a velocity of 34m/s. How far away from the bottom of the cliff does it land?

Discover how to calculate the distance a car lands after driving off a 40m cliff at 34m/s. This solution explores projectile motion concepts and provides a step-by-step analysis. Ideal for high school physics students.

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