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4) A partially filled bag of cement having a mass of 16.0kg falls 40.0m into a river from a bridge. a. What is the kinetic energy of the bag as it hits the water? b. What is its speed just before it hits the water? falls 64.0m. d. What is its new kinetic energy

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4) A partially filled bag of cement having a mass of 16.0kg falls 40.0m into a river from a bridge.
a. What is the kinetic energy of the bag as it hits the water?
b. What is its speed just before it hits the water?
falls 64.0m.
d. What is its new kinetic energy

4) A partially filled bag of cement having a mass of 16.0kg falls 40.0m into a river from a bridge. a. What is the kinetic energy of the bag as it hits the water? b. What is its speed just before it hits the water? falls 64.0m. d. What is its new kinetic energy

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MorrisMaster · Tutor for 5 years

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a. The kinetic energy of the bag as it hits the water is \( KE = \frac{1}{2} \times 16.0 \times (\sqrt{2 \times 9.8 \times 40.0})^{2} \) Joules.<br />b. Its speed just before it hits the water is \( v = \sqrt{2 \times 9.8 \times 40.0} \) m/s.

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## Step 1: Find the kinetic energy<br />To find the kinetic energy (KE) of the bag as it hits the water, we use the formula for kinetic energy:<br /><br />### \( KE = \frac{1}{2} \times m \times v^{2} \)<br /><br />where \( m \) is the mass and \( v \) is the velocity. However, we don't know the velocity yet. To find the velocity, we can use the formula for the final velocity of an object in free fall:<br /><br />### \( v = \sqrt{2gh} \)<br /><br />where \( g \) is the acceleration due to gravity (approximately \( 9.8 \, m/s^{2} \)) and \( h \) is the height from which the object falls. <br /><br />## Step 2: Calculate the velocity<br />Substituting \( g = 9.8 \, m/s^{2} \) and \( h = 40.0 \, m \) into the formula gives us:<br /><br />### \( v = \sqrt{2 \times 9.8 \times 40.0} \)<br /><br />## Step 3: Calculate the kinetic energy<br />Now we can substitute \( m = 16.0 \, kg \) and the calculated velocity into the kinetic energy formula to find the kinetic energy.
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