Until his seventies, Henri LaMothe (Fig. 9-48 ) excited...

Until his seventies, Henri LaMothe (Fig. $9-48$ ) excited audiences by belly-flopping from a height of $12 \mathrm{~m}$ into $30 \mathrm{~cm}$ of water. Assuming that he stops just as he reaches the bottom of the water and estimating his mass, find the magnitude of the impulse on him from the water.

Key Concepts

Momentum

Momentum is a measure of an object’s motion, defined as the product of its mass and velocity. It is a foundational concept in mechanics, often conserved in isolated systems, and plays a key role in analyzing collision and impact scenarios where external impulses alter the momentum of an object.

Free Fall and Energy Conversion

When an object falls under gravity, its gravitational potential energy is converted into kinetic energy. This energy conversion process allows one to determine the velocity just before impact, which is then used to calculate the momentum of the falling object. This concept is important in problems where an object undergoes free fall and then interacts with another medium, requiring the assessment of its change in motion properties.

Impulse-Momentum Theorem

The impulse-momentum theorem relates the impulse applied to an object to the change in its momentum. Impulse is defined as the product of force and the time over which it acts, and it is equal to the difference between the final and initial momentum of the object. This concept is crucial for understanding how forces acting over time produce instantaneous changes in velocity, especially during collision or deceleration scenarios.

Transcript

00:01 So in this question, we're told that henry lomoth excited audiences by belly flopping from a height of 12 meters into 30 centimeters of water.

00:11 Assuming that he stops just as he reaches the bottom of the water and estimating his mass, find the magnitude of the impulse on him from the water.

00:21 So in order to find the impulse j, in this question, we can use the change in my question.

00:31 Momentum, right? so we're going to need to identify, okay, what is the change in momentum here as he makes contact with the water? so if he starts up here and the water is down here, then we need to know what is his speed here when he hits the water.

00:57 And then what is his speed as he just before he reaches the bottom of the water? we'll call that v.

01:05 Ground maybe.

01:05 Well, we know that's zero, because it says, assuming that he stops just as he reaches the bottom of the water.

01:11 Okay, so what we need to do is calculate the change in momentum from that initial point when he hits the water to the bottom of the water.

01:22 Now, in order to calculate this speed when he hits the water, we need to use kinematics.

01:28 Okay, so basically what we can do is, okay, we know that the initial speed right before he jumps is zero, and we can use the following formula, vf.

01:41 Equals v .i squared plus 2ad.

01:53 Now, just before he jumps, his speed is zero.

01:58 And so we can calculate that final velocity just before he hits the water as the square root of 2ad.

02:07 Okay, we know his acceleration is going to be just the acceleration due to gravity.

02:12 That's 9 .81, and the displacement will be 12.

02:16 So once we calculate that, we get a value of about 15 .3 meters per second.

02:24 Now, i know that says the final speed, but that is the speed when he hits the water...

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