Answer:
a

b

Explanation:
From the question we are told that
The child's weight is 
The length of the sliding surface of the playground is 
The coefficient of friction is 
The angle is 
The initial speed is 
Generally the normal force acting on the child is mathematically represented as
=> 
Note 
Generally the frictional force between the slide and the child is

Generally the resultant force acting on the child due to her weight and the frictional force is mathematically represented as

Here F is the resultant force and it is represented as 
=> 
=> 
=> 
=>
So

=> 
Generally the heat energy generated by the frictional force which equivalent tot the workdone by the frictional force is mathematically represented as

=> 
=> 
Generally from kinematic equation we have that

=> 
=> 
=> 