Question

Determine the resultant force at a point (figure 1). Express your answer in terms of the unit vectors i, j, and k. To denote vectors in your answers, be sure to select the 'vec' button.

Answer 1

The resultant force acting on the point with ice skaters pushing is found by adding the vectors F₁ and F₂. The vector sum is 8.0î + 12.0ĵ N, which represents the resultant force on the third skater.

Step-by-step explanation:

To determine the resultant force at a point using vector addition, we need to add the individual force vectors that are acting on that point. Given two ice skaters pushing a third skater with forces represented by the vectors F₁ = 3.0î + 8.0ĵ N and F₂ = 5.0î + 4.0ĵ N, we find the resultant force by adding these two vectors.

The vector sum of F₁ and F₂ is calculated as follows:

Resultant Force (Fnet) = F₁ + F₂

Fnet = (3.0î + 8.0ĵ) + (5.0î + 4.0ĵ)

Fnet = (3.0 + 5.0)î + (8.0 + 4.0)ĵ

Fnet = 8.0î + 12.0ĵ N

Therefore, the resultant force acting on the third skater is 8.0î + 12.0ĵ N.