A ball is thrown upward. What is its initial vertical speed? The acceleration of gravity is 9.8 m/s^2 and maximum height is 7.2 m,. Neglect air resistance. Answer in units of m/s

h = vt - 4.9t^2

max height reached at t=v/9.8 sec
7.2 = v(v/9.8) - 4.9(v/9.8)^2
v = 11.9m/s

To determine the initial vertical speed of the ball, we can use the kinematic equation:

v² = u² + 2as

Where:
v is the final vertical speed (which is 0 m/s at the maximum height)
u is the initial vertical speed (what we're trying to find)
a is the acceleration due to gravity (-9.8 m/s², since it acts in the opposite direction to the motion)
s is the vertical distance traveled (7.2 m)

Plugging in the known values, the equation becomes:

0² = u² + 2(-9.8)(7.2)

Simplifying further:

0 = u² - 141.12

Rearranging the equation to solve for u:

u² = 141.12

Taking the square root of both sides:

u ≈ ±11.88

Since negative velocity indicates the opposite direction of the motion, we can conclude that the initial vertical speed of the ball is approximately 11.88 m/s.

To find the initial vertical speed of the ball, we can use the concept of projectile motion and apply the equation of motion for vertical motion.

In projectile motion, the vertical velocity (speed) of an object changes due to the acceleration of gravity. Since the maximum height is reached when the vertical velocity becomes zero, we can use this information to find the initial vertical speed.

The equation of motion for vertical motion can be written as:
vf^2 = vi^2 + 2as

where:
vf = final vertical velocity (which is 0 m/s at the maximum height)
vi = initial vertical velocity (what we're trying to find)
a = acceleration due to gravity (-9.8 m/s^2)
s = displacement (7.2 m, the maximum height)

Rearranging the equation, we have:
vi^2 = -2as

Plugging in the known values:
vi^2 = -2(-9.8 m/s^2)(7.2 m)

Simplifying this equation, we get:
vi^2 = 141.12 m^2/s^2

Now, to find vi, we can take the square root of both sides:
vi = √(141.12 m^2/s^2)

Calculating this, we find:
vi ≈ 11.88 m/s

Therefore, the initial vertical speed of the ball, neglecting air resistance, is approximately 11.88 m/s.