A 50.2 kg child slides down a water slide with a velocity of 1.1 m/sec at the top. At the bottom of the slide, she is moving horizontally, 1.5 meters above the water. She splashes into the water 2.5 meters to the right of the bottom of the slide.

a) Assuming potential energy to be zero at the water level, what is the mechanical energy of the child at the top of the slide? MEo=

b) How high is the top of the slide above the bottom of the slide?

To find the mechanical energy of the child at the top of the slide and the height of the top of the slide above the bottom, we can use the principle of conservation of energy.

a) The mechanical energy (ME) of an object is the sum of its kinetic energy (KE) and potential energy (PE). At the top of the slide, the child has only kinetic energy since potential energy is taken to be zero at the water level. The formula for kinetic energy is KE = 0.5 * mass * velocity^2.

Plugging in the given values, we have:
Mass (m) = 50.2 kg
Velocity (v) = 1.1 m/s

KEo = 0.5 * (50.2 kg) * (1.1 m/s)^2
MEo = KEo

Now, we can calculate the value of MEo.

b) To find the height of the top of the slide above the bottom, we can use the conservation of energy again. At the top of the slide, the mechanical energy (MEo) is solely in the form of kinetic energy, as potential energy is zero. At the bottom, the mechanical energy is a combination of kinetic and potential energy.

From the conservation of energy principle, we can equate the mechanical energy at the top of the slide (MEo) to the sum of kinetic energy (KE) and potential energy (PE) at the bottom of the slide.

MEo = KE + PE

Since MEo is the same as the calculated value of KEo from part (a), we can write:

KEo = KE + PE

Rearranging the equation, we get:

PE = KEo - KE

Now, we can calculate the value of potential energy (PE) at the bottom of the slide using the formula PE = mass * gravity * height.

Plugging in the given values:
Mass (m) = 50.2 kg
Gravity (g) = 9.8 m/s^2 (approximate value)
Height (h) = ?

PE = (50.2 kg) * (9.8 m/s^2) * h

Since KEo is the same as MEo, we can substitute the value of KEo calculated in part (a) into the equation:

PE = MEo - KE

Finally, we solve for the height (h) by rearranging the equation:

h = (MEo - KE) / ((50.2 kg) * (9.8 m/s^2))

Now, you can substitute the calculated values to find the height (h) of the top of the slide above the bottom.