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:
-----------------------------
| |
| |
| KE | /
| | /
|___________________________| /
1 2 3 height (m)