A bean jumps vertically off of a table. It has a speed of 10 m/s when it reaches half of its maximum height. How high does it rise?
See previous post.
To find the maximum height the bean reaches, we can use the equations of motion.
First, let's define our variables:
- v0: Initial velocity (when it is at the table) = 0 m/s (since it jumps vertically off the table)
- v: Final velocity (when it reaches half of its maximum height) = 10 m/s
- g: Acceleration due to gravity = 9.8 m/s^2
- h: Maximum height reached by the bean
We can use the equation for final velocity (v) in terms of initial velocity (v0), acceleration (a), and distance (d):
v^2 = v0^2 + 2ad
Since the bean is jumping vertically, the displacement (d) can be equated to the maximum height (h) it reaches. Also, since the bean starts with zero initial velocity and accelerates due to gravity, we can substitute these values into the equation:
v^2 = v0^2 + 2gh
Plugging in the values we have:
(10 m/s)^2 = (0 m/s)^2 + 2 * 9.8 m/s^2 * h
100 m^2/s^2 = 19.6 m/s^2 * h
Now, we can solve for h:
h = (100 m^2/s^2) / (19.6 m/s^2)
h ≈ 5.1 meters
Therefore, the bean rises to a height of approximately 5.1 meters.