leiss, work QUESTION 4 (Start on a new pago.) Dancers have to leam many skills, Including how to land correctly. A dancer of mass 50 kg leaps Tnto 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. \( 4.3 \quad \) Calculate the magnitude of the net force acting on the dancer as she lands. Assume that the dancer performs the same jump as before but lands without bending her knees. \( 4.4 \quad \) Will the force. now be GREATER THAN, SMALLER THAN or EQUAL. TO the force calculated in QUESTION 4.3 ? 4.5

To calculate the momentum with which the dancer reaches the ground, you can use the formula for momentum, which is \( p = mv \), where \( m \) is mass and \( v \) is velocity. For our dancer, \( m = 50 \, \text{kg} \) and \( v = 5 \, \text{m/s} \). Plugging in the numbers, we find that the momentum \( p = 50 \times 5 = 250 \, \text{kg m/s} \). This is the momentum she has just before landing, making quite the entrance! Impulse can be defined as the change in momentum or, alternatively, as the product of force and the time duration over which that force acts. This means if there's a big force over a short time (like hitting a wall), or a small force over a long time (like gently pushing a swing), it can produce the same impulse depending on the circumstances. It's all about how to deliver the 'punch' without breaking too much! Now for the force acting on the dancer while landing, we calculate it using the impulse-momentum theorem which states that impulse equals change in momentum. The force can be calculated with the equation: \( F = \Delta p / \Delta t \). The change in momentum (assuming she stops completely) would be her initial momentum (250 kg m/s) and the time to stop is 0.2 s. This yields \( F = 250 / 0.2 = 1250 \, \text{N} \). When the dancer lands without bending her knees, the time to come to a stop decreases drastically. Since impulse depends on time—less time means a more significant force! Thus, the force exerted when landing stiff-legged will be GREATER than the 1250 N calculated when bending her knees. Talk about a tough landing!