A toboggan of mass 8.4 is moving horizontally at 18 . As it passes under a tree, 18 of snow drop onto it.
We're covering Momentum and collisions, and I have no idea where to start here.
The dimensions of the numbers must be specified. That is one of the first things you should have learned when studying physics.
The horizontal momentum of the sled and contents will remain constant, before and after the snow falls on it.
To solve this problem, we need to apply the principle of conservation of momentum. The momentum of an object can be calculated by multiplying its mass (m) by its velocity (v).
Let's break down the problem into two parts: the moment before the snow falls onto the toboggan and the moment after the snow falls onto it.
Before the snow falls, the momentum of the toboggan is given by:
Momentum_before = mass_toboggan * velocity_toboggan
After the snow falls, the momentum of the toboggan and the snow together is given by:
Momentum_after = (mass_toboggan + mass_snow) * velocity_final
According to the principle of conservation of momentum, the total momentum before the snow falls should be equal to the total momentum after the snow falls:
Momentum_before = Momentum_after
Now, let's plug in the given values:
mass_toboggan = 8.4 kg
velocity_toboggan = 18 m/s
mass_snow = 18 kg
Substituting these values into the equations, we get:
mass_toboggan * velocity_toboggan = (mass_toboggan + mass_snow) * velocity_final
Now, we can solve for velocity_final, which represents the final velocity of the toboggan and the snow together:
velocity_final = (mass_toboggan * velocity_toboggan) / (mass_toboggan + mass_snow)
Plugging in the values, we find:
velocity_final = (8.4 kg * 18 m/s) / (8.4 kg + 18 kg)
Simplifying this expression, we get:
velocity_final = 151.2 m/s / 26.4 kg
Finally, calculating the numerical value, we find:
velocity_final ≈ 5.72 m/s
Therefore, the final velocity of the toboggan and the snow together, after the 18 kg of snow fall onto it, is approximately 5.72 m/s.