Which moves faster after being accelerated from rest, (a) a 500 kg boat that has been imparted with a 10,000 N s impulse or (b) a 780 kg boat imparted with a 14,000 N s impulse?

a1 = 10,000/500 = 20 m/s^2

a2 = 14,000/780 = 17.95 m/s^2

500 kg boat moves faster.

Well, let me juggle the numbers for you. Assuming the boats were initially at rest and experienced an impulse, we can use the equation Impulse = mass × change in velocity.

For the first case with the 500 kg boat and a 10,000 N s impulse, we can rearrange the equation to find the change in velocity: change in velocity = Impulse / mass. Plugging in the values, we get change in velocity = 10,000 N s / 500 kg = 20 m/s.

Now, for the second case with the 780 kg boat and a 14,000 N s impulse, we calculate the change in velocity: change in velocity = 14,000 N s / 780 kg ≈ 17.95 m/s.

So, after some clownish calculations, it looks like the 500 kg boat will be moving faster with a speed of 20 m/s, while the 780 kg boat will be lagging behind with a speed of approximately 17.95 m/s. Time to set sail, captain!

To determine which boat moves faster, we can use the principle of conservation of momentum. The momentum of an object is equal to the product of its mass and velocity.

Let's calculate the initial momentum of each boat:

For boat (a):
Mass of the boat, m = 500 kg
Impulse imparted to the boat, J = 10,000 N s

Using the formula for impulse:
J = Δp
Δp = m * Δv

Since the boat starts from rest, the initial velocity (v) is 0. Therefore, we can rewrite the equation as:

J = m * v
v = J / m

Substituting the values:
v = 10,000 N s / 500 kg
v = 20 m/s

Therefore, the initial velocity of boat (a) is 20 m/s.

Now let's calculate the initial velocity of boat (b):

For boat (b):
Mass of the boat, m = 780 kg
Impulse imparted to the boat, J = 14,000 N s

Using the same formula as before:
v = J / m
v = 14,000 N s / 780 kg
v ≈ 17.95 m/s

Therefore, the initial velocity of boat (b) is approximately 17.95 m/s.

Comparing the two boats, we can conclude that boat (a) moves faster after being accelerated from rest. It has an initial velocity of 20 m/s, while boat (b) has an initial velocity of approximately 17.95 m/s.

To determine which boat moves faster after being accelerated from rest, we need to calculate their respective final velocities.

The impulse-momentum relationship states that the impulse imparted to an object is equal to its change in momentum. Mathematically, this can be represented as:

Impulse = Change in Momentum

We can rearrange this equation to solve for the final velocity:

Final Momentum = Initial Momentum + Impulse

Since both boats start from rest, their initial momentum is zero:

Final Momentum = Impulse

Let's calculate the final velocity for each boat using this information:

For boat (a):
Mass = 500 kg
Impulse = 10,000 N s

Using the impulse-momentum equation:
Final Momentum (a) = Impulse = 10,000 N s

Using the definition of momentum:
Final Momentum (a) = Mass (a) * Final Velocity (a)

Rearranging the equation to solve for velocity gives:
Final Velocity (a) = Final Momentum (a) / Mass (a)
Final Velocity (a) = 10,000 N s / 500 kg = 20 m/s

Now let's calculate the final velocity for boat (b):
Mass = 780 kg
Impulse = 14,000 N s

Final Momentum (b) = Impulse = 14,000 N s

Final Velocity (b) = Final Momentum (b) / Mass (b)
Final Velocity (b) = 14,000 N s / 780 kg ≈ 17.95 m/s

Therefore, the boat with a mass of 500 kg and an impulse of 10,000 N s (boat a) moves faster with a final velocity of 20 m/s compared to the boat with a mass of 780 kg and an impulse of 14,000 N s (boat b) which has a final velocity of approximately 17.95 m/s.