Question

A turtle's velocity changes from v1 = 1.0 mm/s at Θ=0°Θ=0° to v2 = 1.2 mm/s at Θ=20°Θ=20°. What is the change in the turtle's velocity? Give the answer in component form (Δv∆vx , Δv∆vy).

Answer 1

The change in the turtle's velocity in component form is calculated by subtracting the initial velocity components from the final velocity components, resulting in (Δvx, Δvy) = (0.226 mm/s, 0.412 mm/s) after accounting for the angle of 20° with respect to the horizontal.

Step-by-step explanation:

To find the change in the turtle's velocity in component form, we need to consider the initial and final velocities given in vector components. The initial velocity vector v1 at 0° is purely in the horizontal direction. Therefore, it has components v1x = 1.0 mm/s and v1y = 0 mm/s. The final velocity vector v2 makes an angle of 20° with the horizontal, which means it has both horizontal and vertical components v2x = v2 cos(20°) and v2y = v2 sin(20°). To calculate the change in velocity (Δv), we subtract the initial velocity components from the final velocity components.

• v2x = 1.2 mm/s cos(20°)
• v2y = 1.2 mm/s sin(20°)

Now we calculate the change in the x and y components:

• Δvx = v2x - v1x
• Δvy = v2y - v1y

We find:

• Δvx = 1.2 mm/s cos(20°) - 1.0 mm/s
• Δvy = 1.2 mm/s sin(20°)

After calculating the trigonometric functions:

• Δvx = 0.226 mm/s
• Δvy = 0.412 mm/s

Therefore, the change in the turtle's velocity in component form is (Δvx, Δvy) = (0.226 mm/s, 0.412 mm/s).