Question

A speedboat moves on a lake with initial velocity vector ₁,x=8.17 m/s and ₁,y=−2.73 m/s , then accelerates for 6.27 s at an average acceleration of av,x=−0.101 m/s² and av,y=0.107 m/s². what are the components of the speedboat's final velocity, ₂,x and ₂,y ? ₂,x = ______ m/s ₂,y = ______ m/s

Answer 1

To find the components of the speedboat's final velocity, add the initial velocity to the change in velocity in each direction.

Step-by-step explanation:

To find the components of the speedboat's final velocity, we need to first find the change in velocity in the x and y directions. The change in velocity in the x direction is given by the formula Δv = av,x * t. Plugging in the values, we get Δv = -0.101 m/s² * 6.27 s. The change in velocity in the y direction is found using the same formula, Δv = av,y * t. Plugging in the values, we get Δv = 0.107 m/s² * 6.27 s.

To find the final velocity in the x direction, we add the initial velocity in the x direction to the change in velocity in the x direction. So the final velocity in the x direction is v₂,x = v₁,x + Δv = 8.17 m/s + (-0.101 m/s² * 6.27 s).

To find the final velocity in the y direction, we add the initial velocity in the y direction to the change in velocity in the y direction. So the final velocity in the y direction is v₂,y = v₁,y + Δv = -2.73 m/s + (0.107 m/s² * 6.27 s).

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