Answer:
The magnitude of her acceleration during her sliding is 5.1m/s² .
Explanation:
The force exerted by the child = mass of the child × acceleration of the child = m × a = ma
but the child slides down at an angle = 42°
The force exerted by the child is inclined; there are 2 other components of child’s force that can be resolved in the plane of inclination, viz:
The horizontal component due to gravity = mgsin42°
The vertical component due to gravity and influenced by kinetic friction of the slide = µmgcos42°
Where g = acceleration due to gravity = 9. 8m/s², and
µ = coefficient of kinetic friction = 0.20
For equilibrium, the sum of forces towards the one direction = the sum of the forces in the opposite direction, thus:
ma + µmgcos42° = mgsin42°
Divide the equation all through by the mass of the child (m), and make the acceleration of the child (a) The subject of the formula, viz:
a = gsin42° — µgcos42°
= (9.8m × sin42°) — (9.8 × 0.2 × cos42°)
= 5.1m/s²