Final answer:
Using the kinematic equation, the rock thrown straight upward with an initial velocity of 6.4 m/s will rise to a height of approximately 2.09 meters. None of the provided options match this calculation, indicating a possible error in the listed choices.
Step-by-step explanation:
To determine the height the rock will rise after being thrown straight upward with an initial velocity of 6.4 m/s, we can use the kinematic equation for uniformly accelerated motion:
0 = v2 - u2 + 2as
Where:
- v is the final velocity (0 m/s at the highest point)
- u is the initial velocity (6.4 m/s)
- a is the acceleration due to gravity (-9.8 m/s2, negative because it's opposite to the direction of motion)
- s is the displacement or the height (which we are looking to find)
Plugging in the values:
0 = (0 m/s)2 - (6.4 m/s)2 + 2(-9.8 m/s2)s
s = (6.4 m/s)2 / (2 * 9.8 m/s2)
s = 40.96 m2/s2 / 19.6 m/s2
s = 2.09 m
Therefore, the rock will rise to a height of approximately 2.09 meters, which is not one of the options provided in the question, indicating a possible typo in the choices. The correct option is not listed.