Jayla drops the same 10-kg ball from heights of 1 m, 2 m, and 3 m. Which graph correctly shows the kinetic energy of the ball that Jayla dropped from each height?
a
4c6e6668-2453-43c1-a0bc-db016672148c.PNG
b
007d1cd7-6750-499c-9690-59428c5940c1.PNG
c
bc8a1e00-6b1e-421a-a2ca-dd77d832f218.PNG
d
5b48dea6-f832-4439-b480-bc98844ab51a.PNG
The correct graph showing the kinetic energy of the ball that Jayla dropped from each height would be option (d). The kinetic energy of the ball is directly proportional to the square of its velocity. As the ball falls, its velocity increases and so does its kinetic energy. The graph in option (d) shows this relationship, with the kinetic energy increasing as the height of the drop increases, and the increase in kinetic energy becoming greater with each successive drop.
Which line graph best shows the relationship between the final velocity of a dropped object (before it hits the ground) and the height from which it is dropped?(1 point)
Responses
Skip to navigation
a student drops the same 10-kilogram bowling ball three separate times. she drops the ball from height of 1 meter 2 meters and 3 meters.
what would a graph showing the kinetic energy from each height look like?
To determine the correct graph showing the kinetic energy of the ball dropped by Jayla from different heights, let's understand the concept of kinetic energy and how it relates to the height of an object.
Kinetic energy (KE) is the energy possessed by an object due to its motion. It is given by the equation KE = (1/2)mv², where m represents the mass of the object and v is its velocity.
When Jayla drops the ball from different heights, the only factor affecting its kinetic energy is the velocity it attains upon impact with the ground. The velocity of an object falling freely under the influence of gravity can be calculated using the equation v = √(2gh), where g is the gravitational acceleration (approximately 9.8 m/s²) and h is the height from which the ball is dropped.
Now let's analyze each graph:
a) 4c6e6668-2453-43c1-a0bc-db016672148c.PNG: This graph shows the kinetic energy increasing with height. However, since the height is increasing linearly, the kinetic energy should increase quadratically (since v² is part of the kinetic energy equation). Therefore, this graph is incorrect.
b) 007d1cd7-6750-499c-9690-59428c5940c1.PNG: This graph shows the kinetic energy increasing quadratically with height. As mentioned earlier, this is the correct relationship between height and kinetic energy, making this graph a possible contender.
c) bc8a1e00-6b1e-421a-a2ca-dd77d832f218.PNG: This graph shows the kinetic energy increasing with height. However, the rate of increase is linear, which is incorrect. Therefore, this graph is also incorrect.
d) 5b48dea6-f832-4439-b480-bc98844ab51a.PNG: This graph shows the kinetic energy decreasing with height. Since the height is increasing, but the kinetic energy is diminishing, this graph incorrectly represents the relationship between height and kinetic energy.
By the process of elimination, option b (007d1cd7-6750-499c-9690-59428c5940c1.PNG) is the correct graph for depicting the kinetic energy of the ball dropped by Jayla from different heights.