Projectile Motion: How Fast Must the Cliff Diver Be Running?

When a cliff diver jumps off a cliff, various factors come into play to determine the safe landing distance. In this scenario, the diver must be running at a specific speed to ensure a safe landing 17.8 meters away from the edge of the cliff.

Understanding Projectile Motion:

Projectile motion involves objects moving in two dimensions under the influence of gravity. In the case of the cliff diver, he follows a parabolic trajectory when jumping off the cliff. The horizontal velocity component of his motion remains constant throughout the jump.

The key to determining the required running speed lies in the horizontal distance the diver must cover before landing. In this case, the diver needs to travel a horizontal distance of 17.8 meters to reach a safe landing spot.

Calculating the Required Running Speed:

To calculate the required running speed, we can use the concept of free fall time. When the diver is in free fall, the time it takes to hit the water can be determined using the equation h = 0.5 * g * t^2, where h is the height from the water, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

By solving for time (t) with a height of 45.1 meters, we find that it takes the diver approximately 3 seconds to reach the water. Since horizontal speed is equal to distance over time (v = d/t), the running speed required before jumping off the cliff can be calculated by dividing the horizontal distance (17.8 meters) by the time (3 seconds), resulting in a speed of 5.9 m/s.

Conclusion:

Therefore, to ensure a safe landing 17.8 meters away from the edge of the cliff, the cliff diver must be running at a speed of 5.9 m/s before making the jump. This speed allows the diver to cover the required horizontal distance within the calculated time frame for a successful landing.