A dolphin experiences a force of 320 N [up]

when it jumps out of the water. The
acceleration of the dolphin is 2.6 m/s
2
[up].
(a) Calculate the mass of the dolphin.
(b) What would be the acceleration of the
dolphin if it had the same strength but half
the mass

F=m₁ a₁ => m₁ =F/a₁ .

If m₂=m₁/2
a₂=F/m₂=F/(m₁/2) =2F/m₁ = 2a₁

(a) To calculate the mass of the dolphin, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

Let's use the formula F = m * a, where F is the force, m is the mass, and a is the acceleration.

Given:
Force (F) = 320 N
Acceleration (a) = 2.6 m/s^2

Rearranging the formula, we get:
m = F / a

Substituting the given values, we get:
m = 320 N / 2.6 m/s^2

Calculating this, we find:
m ≈ 123.08 kg

So, the mass of the dolphin is approximately 123.08 kg.

(b) If the dolphin had the same strength but half the mass, we can calculate the new acceleration using the same formula.

Given:
Force (F) = 320 N
New Mass (m) = 1/2 * 123.08 kg = 61.54 kg

Using the formula F = m * a and rearranging it to solve for acceleration, we get:
a = F / m

Substituting the given values, we get:
a = 320 N / 61.54 kg

Calculating this, we find:
a ≈ 5.20 m/s^2

So, if the dolphin had the same strength but half the mass, the new acceleration would be approximately 5.20 m/s^2.

To calculate the mass of the dolphin, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).

(a) Therefore, we can use the formula F = ma and rearrange it to solve for mass (m):
m = F/a

Given that the force (F) is 320 N and the acceleration (a) is 2.6 m/s² (upward), we can substitute these values into the formula:
m = 320 N / 2.6 m/s²

Calculating this gives us:
m = 123.08 kg

So, the mass of the dolphin is approximately 123.08 kg.

(b) If the dolphin had the same strength (force) but half the mass, we can calculate the new acceleration using the same formula: F = ma.

Given that the force (F) remains the same at 320 N and mass (m) is half of the original mass (61.54 kg), we can substitute these values into the formula:
320 N = (61.54 kg) * a

Now, we can solve for the new acceleration (a):
a = 320 N / 61.54 kg

Calculating this gives us:
a ≈ 5.20 m/s²

So, if the dolphin had the same strength but half the mass, its acceleration would be approximately 5.20 m/s² upwards.

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