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 <em>law of conservation of energy</em>:
Potential Energy Lost = Kinetic Energy Gained
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,
<u>v = 12.13 m/s</u>
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(b)
Using the <em>law of conservation of energy</em>:
Potential Energy Lost = Kinetic Energy Gained
where,
v = speed = ?
g = acceleration due to gravity = 9.81 m/s²
h = height lost = three-fourth way down =
Therefore,
<u>v = 14.86 m/s</u>
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Learn more about the <em>law of conservation</em> of energy here:
brainly.com/question/20971995?referrer=searchResults
The attached picture shows the <em>law of conservation of energy</em>.
