a ball is thrown vertically upward with an initial velocity of 20 m/s? find the height attain by the ball?
v = 20 - 9.8 t
v = 0 at top
9.8 t = 20
h = 20 t - 4.9 t^2
or
m g h = (1/2) m v^2
h = (1/2)v^2/g
To find the height attained by the ball, we need to use the equations of motion for vertical motion.
The equation that relates the height (h), initial velocity (v0), final velocity (vf), and acceleration due to gravity (g) is:
vf^2 = v0^2 + 2gh
In this case, the ball is thrown vertically upward, so the final velocity at its highest point will be zero.
Using this information, we can rearrange the equation to solve for h:
h = (vf^2 - v0^2) / 2g
Since vf is zero, we can simplify the equation to:
h = -v0^2 / (2g)
Plugging in the given values:
v0 = 20 m/s
g = 9.8 m/s^2 (acceleration due to gravity)
h = -20^2 / (2 * 9.8)
Simplifying further:
h = -400 / 19.6
Finally, calculating the height attained by the ball:
h ≈ -20.41 m
The negative sign indicates that the height is measured from the highest point to the original starting point. Thus, the ball reaches a height of approximately 20.41 meters above its initial position.