What impulse does a 3 kg cat sitting on a windowsill 15 m high have? - briefly
The impulse of an object is defined as the change in momentum over time. For a 3 kg cat sitting on a windowsill, the impulse is zero because the cat is at rest and there is no change in its momentum.
What impulse does a 3 kg cat sitting on a windowsill 15 m high have? - in detail
To determine the impulse experienced by a 3 kg cat sitting on a windowsill 15 m high, we need to consider the scenario where the cat falls from the windowsill to the ground. Impulse is defined as the change in momentum, which is the product of mass and velocity. In this scenario, the impulse will be equal to the change in the cat's momentum as it falls to the ground.
First, let's calculate the final velocity of the cat just before it hits the ground. We can use the kinematic equation for free fall:
v = √(2gh)
where:
- v is the final velocity,
- g is the acceleration due to gravity (approximately 9.8 m/s²),
- h is the height from which the cat falls (15 m).
Plugging in the values, we get:
v = √(2 9.8 m/s² 15 m) v = √(294 m²/s²) v ≈ 17.14 m/s
Next, we calculate the momentum of the cat just before it hits the ground. Momentum (p) is given by the product of mass (m) and velocity (v):
p = mv p = 3 kg * 17.14 m/s p ≈ 51.42 kg·m/s
The impulse (J) is equal to the change in momentum. Since the cat starts from rest, its initial momentum is zero. Therefore, the impulse is simply the final momentum:
J = Δp J = p_final - p_initial J = 51.42 kg·m/s - 0 kg·m/s J ≈ 51.42 kg·m/s
Thus, the impulse experienced by the 3 kg cat as it falls from a 15 m high windowsill is approximately 51.42 kg·m/s. This impulse represents the change in momentum that the cat undergoes due to the force of gravity acting over the distance of the fall. It is important to note that this calculation assumes no air resistance and a straight vertical fall. In real-world scenarios, air resistance would reduce the final velocity and thus the impulse.