The kinetic energy of an object just before it hits the ground can be calculated using the formula:
\[ KE = \frac{1}{2} mv^2 \]
where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass of the object (10 kg in this case),
- \( v \) is the velocity of the object just before it hits the ground.
The velocity can be determined using the formula for an object in free fall:
\[ v = \sqrt{2gh} \]
where:
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , m/s^2 \)),
- \( h \) is the height from which the object is dropped.
When we plug in the height values:
-
For \( h = 1 , m \): \[ v = \sqrt{2 \times 9.81 \times 1} \] \[ KE = \frac{1}{2} \times 10 \times (v^2) \]
-
For \( h = 2 , m \): \[ v = \sqrt{2 \times 9.81 \times 2} \] \[ KE = \frac{1}{2} \times 10 \times (v^2) \]
-
For \( h = 3 , m \): \[ v = \sqrt{2 \times 9.81 \times 3} \] \[ KE = \frac{1}{2} \times 10 \times (v^2) \]
The kinetic energy will increase with the height since \( v \) increases with the square root of height. Therefore, the kinetic energy from the three heights would be:
- When dropped from 1 meter, the kinetic energy is the lowest.
- When dropped from 2 meters, it is higher than 1 meter.
- When dropped from 3 meters, it has the highest kinetic energy.
So, the bar graph that accurately reflects this would show the kinetic energy increasing from the height of 1 meter to 2 meters to 3 meters. The bars should represent increasing kinetic energy for these heights in that order. Make sure to select the option that represents this increasing trend correctly.
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