An illustrative scene depicting a situation by a lake. A masculine figure, of White descent and with a body mass corresponding to 70 kilograms, is energetically leaping off a wooden raft. The raft measures approximately 2 square meters and is firmly anchored in a freshwater lake, surrounded by lush trees and a clear sky. Beside the raft, show a measuring tape indicating the changes in water level to depict the potential rise of the raft due to the man's exit. Make sure the image contains no text.

70-kg man jumps off a raft 2 meter squared moored in a freshwater lake. By how much does the raft rise?

Well, if it's a typical raft, I'm pretty sure the only thing that's going to rise is the man's panic level! But on a more serious note, to calculate how much the raft actually rises, we need to know the mass of the raft, the force exerted by the man jumping off it, and any other external factors that might affect it. Without that information, I'm afraid I can't give you a precise answer. But hey, at least we can all have a good laugh imagining a floating raft trying to follow a jumping man!

To calculate how much the raft rises when a 70-kg man jumps off it in a freshwater lake, we can use the principle of buoyancy.

Step 1: Calculate the weight of the man:
The weight of an object can be calculated using the formula:
Weight = mass × gravitational acceleration
Given that the mass of the man is 70 kg and the gravitational acceleration is approximately 9.81 m/s², we can calculate the weight of the man:
Weight = 70 kg × 9.81 m/s² = 686.7 N

Step 2: Calculate the buoyant force acting on the raft:
The buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by that object.
Since the man is now in the water, he displaces some water equal to his volume. The volume of water displaced can be calculated using the formula:
Volume = mass / density
The density of freshwater is approximately 1000 kg/m³, so the volume of water displaced is:
Volume = 70 kg / 1000 kg/m³ = 0.07 m³

The buoyant force can be calculated using the formula:
Buoyant force = volume × density of water × gravitational acceleration
Buoyant force = 0.07 m³ × 1000 kg/m³ × 9.81 m/s² = 686.7 N

Step 3: Calculate the rise of the raft:
The rise of the raft is equal to the weight of the man minus the buoyant force acting on the raft. Mathematically, it can be expressed as:
Rise = Weight - Buoyant force
Rise = 686.7 N - 686.7 N = 0 N

Therefore, the raft does not rise when the man jumps off it.

To determine how much the raft rises when the man jumps off, we need to apply the principle of conservation of momentum.

The initial momentum of the system, consisting of the man and the raft, is zero since the man is initially at rest on the raft. When the man jumps off, he gains momentum in the opposite direction. According to Newton's third law of motion, for every action, there is an equal and opposite reaction.

Using the equation:

m1v1 = -m2v2

where m1 is the mass of the man, v1 is the initial velocity of the man-raft system, m2 is the mass of the man, and v2 is the final velocity of the man.

Given that the mass of the man is 70 kg, we can assume that the mass of the raft is negligible compared to the man's mass, so we can ignore it in our calculations. Also, since the initial velocity is zero, we have:

0 = -70 kg * v2

Simplifying the equation, we find:

v2 = 0 m/s

This means that the final velocity of the man is zero after he jumps off the raft. As a result, the raft does not rise at all when the man jumps off.

Step by Step did it right

change in buoyant force = density of water * g * additional area of waterplane * distance it sinks

m=70kg(1kg/1000m3)

=.07m3

A=2m sq. =4m
H=V/A

h=0.07m3/4m2
=0.018m or 1.8cm