Question

You drop a 579 g piece of pizza onto the floor. The impulse of the collision of the pizza with the floor was 2.57 N s. From what height did you drop it? Express your answer in metres to two decimal places.

Answer 1

To calculate the initial height from which a 579 g pizza was dropped based on an impulse of 2.57 N s, convert the mass to kg, use impulse to find the initial velocity, and employ the free-fall kinematic equation with gravity to find the height.

Step-by-step explanation:

You are asking about the height from which a 579 g piece of pizza was dropped, given an impulse of 2.57 N s during its collision with the floor. To find the initial height, we first need to calculate the velocity of the pizza just before it strikes the floor using impulse. Impulse (I) equals the change in momentum (Δp), which in turn is the mass (m) times the change in velocity (Δv): I = m * Δv. Since the pizza comes to a rest when hitting the floor, its final velocity is 0 and the impulse equals the initial momentum of the pizza.

First, we convert the mass to kilograms by dividing by 1000: 579 g / 1000 = 0.579 kg. Then we can solve for the initial velocity (v_i) using the impulse: I = m * v_i, so v_i = I / m = 2.57 N s / 0.579 kg. After calculating the velocity, we use the kinematic equation for free fall (v^2 = 2 * g * h) to find the initial height (h), where g is the acceleration due to gravity (9.8 m/s²). After calculating h, we'll express the answer in metres to two decimal places.