Final answer:
The potential energy of a 2 kg body thrown upwards with an initial velocity of 20 m/s at the end of 2 seconds is 399.84 J. However, this value does not match any of the provided answer choices, suggesting there may be a mistake in the provided options or in the assumptions of the question.
Step-by-step explanation:
To calculate the potential energy of a 2 kg body thrown vertically upwards with an initial velocity of 20 m/s at the end of 2 seconds, we first need to determine the height it reached at that time. Using the kinematic equation:
h = ut + (1/2)at^2, where:
- u is the initial velocity (20 m/s),
- a is the acceleration due to gravity (-9.8 m/s^2, negative because it is in the opposite direction of the initial velocity), and
- t is the time (2 s).
Plugging the values in:
h = (20 m/s)(2 s) + (1/2)(-9.8 m/s^2)(2 s)^2,
h = 40 m - 19.6 m,
h = 20.4 m.
Now, we calculate the potential energy (PE) using the formula:
PE = mgh, where:
- m is the mass (2 kg),
- g is acceleration due to gravity (9.8 m/s^2),
- h is the height (20.4 m).
PE = (2 kg)(9.8 m/s^2)(20.4 m),
PE = 399.84 J.
However, since this energy value is not an option in the multiple-choice answers provided, and assuming no other forces are acting such as air resistance, it's possible that there is an error in the provided choices or in the initial assumptions of the question.