A 1kg ball is tossed straight up with a kinetic energy of 196J. How high does it go.

20m

KE = M*Vo^2/2 = 196 J.

1*Vo^2/2 = 196
Solve for Vo.

V^2 = Vo^2 + 2g*h = 0 @ max ht.
h = -Vo^2/2g. g = -9.8 m/s^2
Solve for h.

To determine the height the 1kg ball reaches when it is tossed straight up with a kinetic energy of 196J, we need to use the principle of conservation of energy.

The initial kinetic energy (KE) of the ball is equal to the potential energy (PE) when it reaches its highest point, given that there is no significant energy loss due to air resistance.

The formula for kinetic energy is given by:

KE = 0.5 * mass * velocity^2

Given that the mass (m) of the 1kg ball is 1kg and the kinetic energy (KE) is given as 196J, we can rearrange the formula to find the initial velocity (v) of the ball:

KE = 0.5 * m * v^2
196 = 0.5 * 1 * v^2
196 = 0.5 * v^2
392 = v^2
v = sqrt(392)
v ≈ 19.80 m/s

Next, we can determine the maximum height (h) the ball reaches using the formula for potential energy:

PE = mass * gravity * height

The potential energy (PE) at the highest point when the velocity is zero is equal to the initial kinetic energy:

PE = KE = 196J
mass * gravity * height = 196
1 * 9.8 * h = 196
9.8h = 196
h = 196 / 9.8
h ≈ 20 meters

Therefore, the height the 1kg ball reaches when it is tossed straight up with a kinetic energy of 196J is approximately 20 meters.

To determine the height the 1kg ball reaches, we need to use the principle of conservation of energy. We know that the initial kinetic energy of the ball is 196J.

The total mechanical energy of the ball remains constant throughout its motion, so when the ball reaches its peak height, its kinetic energy will be zero. At this point, all of the initial kinetic energy will be converted into gravitational potential energy.

The formula for gravitational potential energy is given by the equation:

Potential Energy = mass * gravity * height

where
- mass is the mass of the object (1kg in this case)
- gravity is the acceleration due to gravity, which is approximately 9.8 m/s² on Earth
- height is the vertical distance from the ground to the highest point the ball reaches

Since the kinetic energy is fully converted into potential energy at the highest point, we can equate them:

Kinetic Energy = Potential Energy

196J = mass * gravity * height

Substituting the known values:

196J = 1kg * 9.8 m/s² * height

Now, we can rearrange the equation to solve for the height:

height = 196J / (1kg * 9.8 m/s²)

Calculating the expression:

height = 20m

Therefore, the 1kg ball will reach a height of 20 meters.