To determine the kinetic energy of the bowling ball when dropped from different heights, we can use the formula for gravitational potential energy, which converts to kinetic energy just before the ball hits the ground:
\[ PE = mgh \]
Where:
- \(PE\) is the potential energy (which will equal the kinetic energy just before impact),
- \(m\) is the mass of the ball (10 kilograms),
- \(g\) is the acceleration due to gravity (approximately \(9.8 , m/s^2\)),
- \(h\) is the height from which the ball is dropped.
Calculating the potential energy (and hence kinetic energy) from each height:
-
From 1 meter: \[ PE = 10,kg \times 9.8,m/s^2 \times 1,m = 98,J \]
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From 2 meters: \[ PE = 10,kg \times 9.8,m/s^2 \times 2,m = 196,J \]
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From 3 meters: \[ PE = 10,kg \times 9.8,m/s^2 \times 3,m = 294,J \]
The kinetic energy at the point of impact will therefore be as follows:
- From 1 meter: 98 Joules
- From 2 meters: 196 Joules
- From 3 meters: 294 Joules
In a graph plotting height on the x-axis and kinetic energy on the y-axis, you would expect to see a linear increase in the kinetic energy corresponding to the height of the drop.
The values would translate to:
- At height 1m: 98 J
- At height 2m: 196 J
- At height 3m: 294 J
The correct graph should show a straight line increasing from left to right with these points plotted.
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