To determine the height of a stone thrown directly upward at an initial velocity of 10 m/s, we can use the kinematic equation that relates the final velocity, initial velocity, acceleration, and displacement.
In this case, since the stone is thrown directly upward, the acceleration acting on the stone is the acceleration due to gravity (g) in the downward direction, which is approximately 9.8 m/s² (assuming no air resistance).
The kinematic equation we can use is:
vf^2 = vi^2 + 2ad
Where:
- vf is the final velocity,
- vi is the initial velocity,
- a is the acceleration, and
- d is the displacement.
Since the stone reaches its highest point, the final velocity (vf) will be zero when it momentarily stops before falling back down.
Plugging in the given values:
0^2 = (10 m/s)^2 + 2(-9.8 m/s²)d
Simplifying the equation:
0 = 100 m²/s² - 19.6 m/s²d
Rearranging the equation to solve for d:
19.6 m/s²d = 100 m²/s²
d = 100 m²/s² / 19.6 m/s²
d ≈ 5.1 m
Therefore, the height of the stone thrown directly upward with an initial velocity of 10 m/s is approximately 5.1 meters.