A 30 kg child steps to a dock from a 60 kg boat,giving the boat an acceleration of 2m/s^2. Neglecting water Resistance, the acceleration experienced by the child is?
-4 m/s^2
To determine the acceleration experienced by the child, we can analyze the forces acting on the child-boat system.
Let's denote the acceleration of the child as a_child and the acceleration of the boat as a_boat.
According to Newton's second law, the net force acting on an object is equal to the product of its mass and acceleration.
For the child:
Net force on the child = Mass of the child * Acceleration of the child
F_child = m_child * a_child
For the boat:
Net force on the boat = Mass of the boat * Acceleration of the boat
F_boat = m_boat * a_boat
Since the child and the boat are connected, the net force acting on them is the same. Therefore, we can equate the forces acting on the child and the boat:
F_child = F_boat
m_child * a_child = m_boat * a_boat
Now, let's substitute the given values into the equations:
m_child * a_child = 60 kg * 2 m/s^2
30 kg * a_child = 120 kg·m/s^2
a_child = (120 kg·m/s^2) / 30 kg
a_child = 4 m/s^2
The acceleration experienced by the child is 4 m/s^2.