Question

A 22.0-kg child descends a slide 1.90 m high and reaches the bottom with a speed of 1.30 m/s __________.

Options:
Option 1: 0.675 m/s
Option 2: 1.125 m/s
Option 3: 1.500 m/s
Option 4: 2.250 m/s

Answer 1

Using the principle of conservation of energy, the child reaches the bottom of the slide with a speed of 6.16 m/s. The correct option is not given.

Step-by-step explanation:

To solve this problem, we can use the principle of conservation of energy. The potential energy of the child at the top of the slide is converted into kinetic energy at the bottom of the slide.

First, we need to calculate the potential energy of the child at the top of the slide using the formula:

Potential energy = mass * gravity * height

Plugging in the values, we have:

Potential energy = 22.0 kg * 10 m/s² * 1.90 m = 418 J

Next, we can use the formula for kinetic energy:

Kinetic energy = 0.5 * mass * velocity²

Plugging in the values, we have:

418 J = 0.5 * 22.0 kg * velocity²

Simplifying the equation, we get:

velocity² = 418 J / (0.5 * 22.0 kg) = 38 J/kg

Taking the square root of both sides, we find:

velocity = √(38 J/kg) = 6.16 m/s

Therefore, the child reaches the bottom of the slide with a speed of 6.16 m/s.