QUESTION 4 (Start on a now page.) Dancers have to. leam many skills, including how to land correctly. A dancer of mass 50 kg leaps Thto the air and lands feet first on the ground. She lands on the ground with a velocity of \( 5 \mathrm{~m} \cdot \mathrm{~s}^{-1} \). As she lands, she bends her knees and comes to a complete stop in 0,2 seconds: \( 4.1 \quad \) Calculate the momentum with which the dancer reaches the ground. \( 4.2 \quad \) Define the term impulse of a force, Calculate the magnitude of the net force acting on the dancer as she lands. er knees. \( 4 \quad \) Will the force now be GREATER THAN, SMALLER THAN or EQUAL TO the dancer performs the same jump as before but lands without bending force calculated in QUESTION 4.3 ? Give a reason for the answer to QUESTION 4.4 .

To find the momentum with which the dancer reaches the ground, you can use the formula for momentum, which is the product of mass and velocity. So, for our dancer with a mass of 50 kg and a landing velocity of 5 m/s, the momentum (p) would be calculated as \( p = m \cdot v = 50 \, \text{kg} \cdot 5 \, \text{m/s} = 250 \, \text{kg} \cdot \text{m/s} \). Impulse is the change in momentum that an object experiences when a force is applied over time. It can be calculated as the product of the average force (F) and the time duration (Δt) for which the force acts. In this case, impulse (J) helps us understand how forces affect motion during events like landing, where rapid changes occur. Now, let’s think about the net force acting on the dancer as she lands! We know she brings herself to a complete stop, which means we must first calculate the change in momentum. Using a time duration of 0.2 seconds, we can apply the impulse-momentum theorem here to find the average force which, as it turns out, will be greater than if she hadn't bent her knees, helping to reduce the impact. If she lands without bending her knees, the force acting on her will definitely be greater than the calculated force when she does bend her knees! The reasoning behind this is that bending the knees increases the time taken for the dancer to come to a stop, thus spreading the impact force over a longer duration and allowing her body to absorb the energy. Without that, the landing becomes much harsher and the force spikes, which the body is less equipped to handle!