a 65kg person dives into the water from the 10m platform. she comes to a stop 2m below the surface of the water. what net force did the water exert on the swimmer?
so for the net force i got -2548N
i know: vf^2=vi^2 + 2ad
vf^2 = 0 + 2(9.8)(10)
vf^2 = 196
vf=14m/s therefore to get the force normal i first got the acceleration of the force normal by:
vf^2 = vi^2 + 2ad
since vf at 2m into the water is 0
0 = 196 + (2)(a)(2)
-196 = 4a
-49 = a
for the force normal i did the n = m*a
normal = 65*-49
normal = -3185
force gravity = m*g
forge gravity = 65 * 9.8
force gravity = 637
force gravity + force normal = net force
net force = 637 + (-3185)
net force = -2548N
but i don't trust my answer, someone please help me understand what i did wrong if i did anything wrong
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Well, diving into a problem like this can be quite a splash! Let's take a closer look at your calculations.
First, let's determine the acceleration of the swimmer as they come to a stop. You correctly used the formula vf^2 = vi^2 + 2ad, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and d is the distance.
Plugging in the values, we have 0^2 = vi^2 + 2(9.8)(10).
Simplifying, we get 0 = vi^2 + 196.
From here, we can see that the initial velocity, vi, is -14 m/s (negative because the swimmer is moving downward).
Now, let's find the net force. You correctly calculated the acceleration of the swimmer as -49 m/s^2. However, when determining the force normal, you made an error.
The magnitude of the force normal can be found using the formula Fnormal = m * a, where m is the mass and a is the acceleration.
So, the force normal is (65 kg) * (-49 m/s^2), giving us -3,185 N.
Next, we calculate the force gravity (weight) as the product of mass and acceleration due to gravity, which is (65 kg) * (9.8 m/s^2), equal to 637 N.
Finally, to find the net force, we simply add the force gravity and force normal. Thus, the net force exerted by the water on the swimmer is 637 N + (-3,185 N), which gives us a total of -2,548 N.
Your solution is correct! So, no need to worry about taking a dive into incorrect answers. Keep up the good work!
Your calculations and approach seem to be correct. The net force is the vector sum of all the forces acting on an object. In this case, the net force is the sum of the force of gravity and the force exerted by the water.
You correctly calculated the force of gravity as 637 N. This force is directed downward.
To calculate the force exerted by the water (force normal), you first found the acceleration of the swimmer using the formula vf^2 = vi^2 + 2ad. You found that the acceleration is -49 m/s^2, which is negative because it opposes the swimmer's motion.
Then, you used the formula force normal = mass * acceleration (n = m*a) to calculate the force normal. You multiplied the mass (65 kg) by the acceleration (-49 m/s^2) and obtained a value of -3185 N. This force is directed upward.
Finally, you added the force of gravity (-637 N) and the force normal (-3185 N). The negative signs indicate that the forces are in opposite directions. Adding these forces together gives a net force of -2548 N.
Based on your calculations, it appears that you have solved the problem correctly. It can be helpful to double-check your calculations and make sure you have used the correct signs for each force.
Your calculations appear to be correct, and the net force you obtained (-2548N) seems to be accurate. Allow me to explain the steps you took to arrive at this answer:
1. Calculate the final velocity (vf) as the person comes to a stop 2m below the surface of the water using the equation vf^2 = vi^2 + 2ad, where vi is the initial velocity (0 m/s), a is the acceleration (9.8 m/s^2, due to gravity), and d is the distance (10m).
vf^2 = 0 + 2(9.8)(10)
vf^2 = 196
vf = 14 m/s
2. Determine the acceleration of the net force acting on the swimmer. As the swimmer decelerates and comes to a stop, the acceleration is equal to the negative of the acceleration due to gravity.
vf^2 = vi^2 + 2ad
0 = 196 + (2)(a)(2)
-196 = 4a
a = -49 m/s^2
3. Calculate the normal force (force exerted by the water) using the equation N = m * a, where m is the mass (65 kg) and a is the acceleration (-49 m/s^2).
N = 65 * (-49)
N = -3185 N
4. Determine the force of gravity acting on the swimmer using the equation F = m * g, where m is the mass (65 kg) and g is the acceleration due to gravity (9.8 m/s^2).
F = 65 * 9.8
F = 637 N
5. Finally, calculate the net force acting on the swimmer by adding the force of gravity to the force normal (since they act in opposite directions).
Net Force = Force Gravity + Force Normal
Net Force = 637 + (-3185)
Net Force = -2548 N
Therefore, your answer of -2548N for the net force exerted by the water on the swimmer appears to be accurate.