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(e) As the boat passes over a wave, the gravitational potential energy of the boat increases by 19600 J. mass of boat=8000kg gravitational field strength=9.8N/kg Calculate the change in height of the centre of mass of the boat as it passes ov the wave.

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(e) As the boat passes over a wave, the gravitational potential energy of the boat
increases by 19600 J.
mass of boat=8000kg
gravitational field strength=9.8N/kg
Calculate the change in height of the centre of mass of the boat as it passes ov
the wave.

(e) As the boat passes over a wave, the gravitational potential energy of the boat increases by 19600 J. mass of boat=8000kg gravitational field strength=9.8N/kg Calculate the change in height of the centre of mass of the boat as it passes ov the wave.

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NancyExpert · Tutor for 3 years

Answer

The change in height of the center of mass of the boat as it passes over the wave is \(0.25 \mathrm{~m}\).

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## Step 1: We are given the increase in gravitational potential energy (\(\Delta U\)) as \(19600 \mathrm{~J}\), the mass of the boat (\(m\)) as \(8000 \mathrm{~kg}\), and the gravitational field strength (\(g\)) as \(9.8 \mathrm{~N} / \mathrm{kg}\). We are asked to find the change in height (\(\Delta h\)) of the center of mass of the boat.<br /><br />## Step 2: We can use the formula for gravitational potential energy to find the change in height. The formula is:<br />### \(\Delta U = m \cdot g \cdot \Delta h\)<br /><br />## Step 3: Rearrange the formula to solve for \(\Delta h\):<br />### \(\Delta h = \frac{\Delta U}{m \cdot g}\)<br /><br />## Step 4: Substitute the given values into the formula:<br />### \(\Delta h = \frac{19600 \mathrm{~J}}{8000 \mathrm{~kg} \cdot 9.8 \mathrm{~N} / \mathrm{kg}}\)<br /><br />## Step 5: Calculate the quotient to get the change in height:<br />### \(\Delta h = \frac{19600}{78400}\)<br />### \(\Delta h = 0.25 \mathrm{~m}\)
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