Final answer:
The mouse's resultant displacement after moving north and then west is approximately 11.18 m. The mouse's velocity is 2.795 m/s at an angle of 26.57° west of north.
Step-by-step explanation:
The question asks for the velocity of a mouse that covers a displacement in two segments: 10.0 m north and 5.0 m west, in 4.0 seconds. Since velocity is a vector quantity, we must first calculate the resultant displacement of the mouse and then divide this by the time taken to get the velocity.
To find the resultant displacement, we can use the Pythagorean theorem because the north and west segments are perpendicular to each other:
√(10.0 m)² + (5.0 m)² = √125 = 11.18 m (correct to two decimal places)
Now, to find the magnitude of the velocity, we divide the resultant displacement by the time:
11.18 m / 4.0 s = 2.795 m/s
To find the direction, the angle θ can be calculated using the tangent function:
θ = arctan(opposite/adjacent) = arctan(5.0 m / 10.0 m) = arctan(0.5) ≈ 26.57°
So, the direction of the velocity vector is 26.57° west of north.
The mouse's velocity is therefore 2.795 m/s at an angle of approximately 26.57° west of north.