# The Cliff Diver - Projectile motion

• Bottomsouth
In summary, the swimmer must have a minimum horizontal speed of 1.08 m/s at the top of the cliff in order to miss the ledge at the bottom, assuming a downward acceleration of 9.8 m/s^2. This is found by solving for the time in the first equation and substituting it into the second equation to find the initial horizontal velocity.
Bottomsouth

## Homework Statement

A swimmer dives off a cliff with a running horizontal leap. What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom which is 1.5 m wide and 9.5m below the top of the cliff.

## Homework Equations

X=V0xT Y=-1/2gt^2

## The Attempt at a Solution

I have X=1.5 and Y=9.5

9.5=-1/2*9.8*t^2
1.5=V0x*t

From there I am lost, I've tried squaring T and so on. Any help is appreciated.

Solve the first equation for the time. Substitute it into the second to find the Vo.

9.5=-1/2*9.8*t^2
9.5=-4.9*t^2
1.93=t^2
t=1.389

1.5=Vox*1.389
1.08=Vox

Does this sound right?

Looks good!
In case your marker is picky, it would be a good idea to deal with the extra minus sign in the first part. Either think of "down" as positive and not use any minus signs, or put a minus sign on the 9.5 to indicate it is down.

## 1. What is projectile motion?

Projectile motion is the motion of an object through the air, where the only force acting on the object is gravity. This results in a curved path known as a parabola.

## 2. How is projectile motion related to cliff diving?

Cliff diving involves jumping off a high platform or cliff into a body of water. Since the diver is in the air for a short period of time, their motion can be described as a projectile motion.

## 3. What factors affect the trajectory of a cliff diver?

The trajectory of a cliff diver is affected by the initial launch velocity, angle of launch, air resistance, and the force of gravity. These factors determine the shape and distance of the diver's path.

## 4. How is the distance of a cliff dive measured?

The distance of a cliff dive is measured from the point of takeoff to the point of entry into the water. This distance is influenced by the height of the cliff, the angle of launch, and the initial velocity of the diver.

## 5. Can the trajectory of a cliff diver be predicted accurately?

Yes, the trajectory of a cliff diver can be predicted accurately using the laws of physics and mathematical equations such as the equations of motion. However, external factors such as wind or the diver's body position can affect the trajectory and make it difficult to predict with 100% accuracy.

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