Question

At the center of a 50-m-diameter circular ice rink, a 76 kg skater traveling north at 2.3 m/s collides with and holds onto a 63 kg skater who had been heading west at 3.9 m/s. What is the final velocity of the skaters after the collision?

Answer 1

The problem is a conservation of momentum problem in Physics, where the final velocity of two colliding and merging skaters is calculated by equating initial and final momentum components in two dimensions and combining them to get the resultant final velocity.

Step-by-step explanation:

The question involves a conservation of momentum problem typically found in Physics. When two skaters collide and hold onto each other, the final velocity can be calculated by using the law of conservation of momentum, which states that the total momentum of a closed system is conserved if no external forces act on it. In this scenario, we will assume an isolated system where external forces are negligible.

To solve this, we apply the conservation of linear momentum formula:

• p_initial = p_final

Which expands to:

• m1 * v1 + m2 * v2 = (m1 + m2) * v_final

Here, m1 and m2 are the masses, v1 and v2 are the initial velocities, and v_final is the final velocity of the merged skaters. We must consider the northward and westward directions as perpendicular to each other, making this a two-dimensional problem. We handle each direction separately using components and then combine them to find the resultant velocity.

The final velocity's magnitude |v_final| is found by:

• |v_final| = sqrt(v_final_x^2 + v_final_y^2)

Where v_final_x and v_final_y are the final velocity components in the x-axis (west-east) and y-axis (south-north) respectively.