A 2.3-kg body is initially moving northward at 15 m/s. Then a force of 12 N, toward the east, acts on it for a time of 2.2 s.(a) At the end of that time, what is the body's final velocity?

To solve this problem, we'll use the formula for force, F = ma, where F is force, m is mass, and a is acceleration. We'll also use the formula for final velocity, v = u + at, where v is final velocity, u is initial velocity, a is acceleration, and t is time.

Step 1: Calculate the acceleration. We know the force (F) is 12 N and the mass (m) is 2.3 kg. We can rearrange the formula F = ma to solve for a: a = F/m. So, a = 12 N / 2.3 kg = 5.22 m/s². This is the acceleration eastward.

Step 2: Calculate the final velocity in the eastward direction. The initial velocity (u) in the eastward direction is 0 (since the body was initially moving northward), the acceleration (a) is 5.22 m/s² (as calculated above), and the time (t) is 2.2 s. So, v = u + at = 0 + 5.22 m/s² * 2.2 s = 11.48 m/s. This is the final velocity in the eastward direction.

Step 3: Combine the initial northward velocity with the final eastward velocity. The body was initially moving northward at 15 m/s and finally moving eastward at 11.48 m/s. These two velocities are perpendicular to each other, so we can use the Pythagorean theorem to find the resultant velocity: v = sqrt((15 m/s)² + (11.48 m/s)²) = 18.9 m/s.

So, the body's final velocity is 18.9 m/s.