A student drops the same 10 kilogram bowling ball three separate times. She drops the ball from heights of 1 meter, 2 meters, and 3 meters. Which graph correctly shows the ball’s kinetic energy when dropped from each height?
Since the kinetic energy of an object is given by the formula:
KE = 1/2 * mass * velocity^2,
we can determine the velocity of the ball right before it hits the ground by using the formula for gravitational potential energy:
PE = mass * g * height,
where g is the acceleration due to gravity (approximately 9.8 m/s^2). We can rearrange this equation to solve for velocity:
velocity = sqrt(2 * g * height).
Plugging in the values for each height, we have:
velocity_1 = sqrt(2 * 9.8 * 1) = 4.43 m/s,
velocity_2 = sqrt(2 * 9.8 * 2) = 6.26 m/s,
velocity_3 = sqrt(2 * 9.8 * 3) = 7.67 m/s.
Therefore, the kinetic energy of the ball when dropped from each height is as follows:
KE_1 = 1/2 * 10 * (4.43)^2 = 97.88 Joules,
KE_2 = 1/2 * 10 * (6.26)^2 = 196.23 Joules,
KE_3 = 1/2 * 10 * (7.67)^2 = 369.06 Joules.
We can now plot these values on a graph. Here, the x-axis represents the height (in meters), and the y-axis represents the kinetic energy (in Joules). The graph should show an increasing trend since the kinetic energy depends on the square of the velocity.
Below is the graph that correctly shows the ball's kinetic energy when dropped from each height:
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1 2 3 height (m)
what is the height of 1, 2, and 3
is it 20, 100, 200, or 300
The height mentioned in the question is 1 meter, 2 meters, and 3 meters. So the correct heights are 1, 2, and 3. The options 20, 100, 200, and 300 are not mentioned in the original question and are not relevant to this specific problem.
what is the height of 1 2 and 3
The heights mentioned in the question are 1 meter, 2 meters, and 3 meters.
what is the kenetic energy to 1 2 and 3
To find the kinetic energy for each height, we need to use the formula:
KE = 1/2 * mass * velocity^2.
The mass of the bowling ball is given as 10 kilograms.
Using the previously calculated velocities:
velocity_1 = 4.43 m/s,
velocity_2 = 6.26 m/s,
velocity_3 = 7.67 m/s.
We can calculate the kinetic energy for each height:
KE_1 = 1/2 * 10 * (4.43)^2 = 97.88 Joules,
KE_2 = 1/2 * 10 * (6.26)^2 = 196.23 Joules,
KE_3 = 1/2 * 10 * (7.67)^2 = 369.06 Joules.