If the mass is 4.3 kg, the initial speed is 4.0 m/s, and the initial height is 8.4 m, find the speed of the ball when it is at a height of 8.0 m.

Please and Thank You for the help.

I assume it is going straight up.

v = 4 - 9.8 t

8 = 8.4 + 4 t - 4.9 t^2

you can solve the soecond for t with quadratic equation (take the positive t) and then use the first equation to find v
However it is easier to use energy
(1/2)m v^2 + m g h = constant
cancel m It does not matter, rock same as feather here.
(1/2)(4^2) + 9.8(8.4) = (1/2)v^2 + 9.8(8)

In what direction is it launched? Straight down? It makes a dofference. The mass will not matter.

You may have omitted part of the question.

I do not think it matters in the end if straight up or straight down, but at some intermediate angle is no good.

To find the speed of the ball when it is at a height of 8.0 m, we can use the principle of conservation of mechanical energy. The mechanical energy of the ball is conserved when the only forces acting on it are conservative forces, such as gravity.

The mechanical energy of the ball is the sum of its kinetic energy (KE) and potential energy (PE):

Total mechanical energy (E) = KE + PE

At the initial height, the ball has gravitational potential energy (GPE) and no kinetic energy:

E1 = KE1 + PE1 = 0 + m * g * h1

Where m is the mass of the ball, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h1 is the initial height.

When the ball is at a height of 8.0 m, it has potential energy and kinetic energy:

E2 = KE2 + PE2

We can set the total mechanical energy at both heights equal to each other because energy is conserved:

E1 = E2

m * g * h1 = KE2 + PE2

In this case, we want to find the speed (v2) of the ball when it is at a height of 8.0 m, which is the kinetic energy at that point.

To find KE2, we can subtract PE2 from E2:

KE2 = E2 - PE2

Substituting the formula for total mechanical energy and potential energy, the equation becomes:

m * g * h1 = KE2 + m * g * h2

Where h2 is the height of 8.0 m and KE2 is the kinetic energy (v2) at that point.

Now, solve for v2:

v2 = sqrt(2 * g * (h1 - h2))

Substituting the given values:

v2 = sqrt(2 * 9.8 * (8.4 - 8.0))

v2 = sqrt(2 * 9.8 * 0.4)

v2 = sqrt(7.84)

v2 ≈ 2.8 m/s

Therefore, the speed of the ball when it is at a height of 8.0 m is approximately 2.8 m/s.