This question involves the concept of the conservation of energy.
(a) The child's speed halfway will be "12.13 m/s".
(b) The child's speed three-fourth way will be "14.86 m/s".
(a)
Using the law of conservation of energy:
Potential Energy Lost = Kinetic Energy Gained
[tex]mgh = \frac{1}{2}mv^2\\\\2gh = v^2\\\\v = \sqrt{2gh}[/tex]
where,
v = speed = ?
g = acceleration due to gravity = 9.81 m/s²
h = height lost = halfway = height/2 = 15 m/2 = 7.5 m
Therefore,
[tex]v = \sqrt{(2)(9.81\ m/s^2)(7.5\ m)}[/tex]
v = 12.13 m/s
(b)
Using the law of conservation of energy:
Potential Energy Lost = Kinetic Energy Gained
[tex]mgh = \frac{1}{2}mv^2\\\\2gh = v^2\\\\v = \sqrt{2gh}[/tex]
where,
v = speed = ?
g = acceleration due to gravity = 9.81 m/s²
h = height lost = three-fourth way down = [tex]\frac{3}{4}height = \frac{3}{4}(15\ m) = 11.25\ m[/tex]
Therefore,
[tex]v = \sqrt{(2)(9.81\ m/s^2)(11.25\ m)}[/tex]
v = 14.86 m/s
Learn more about the law of conservation of energy here:
https://brainly.com/question/20971995?referrer=searchResults
The attached picture shows the law of conservation of energy.
