A snowmobile is originally at the point with position vector 31.5 m at 95.0° counterclockwise from the x axis, moving with velocity 4.29 m/s at 40.0°. It moves with constant acceleration 1.82 m/s2 at 200°. After 5.00 s have elapsed, find the following.

see other post.

To find the following quantities, we need to analyze the motion of the snowmobile using vector addition and kinematic equations. Let's go through each of the quantities step by step.

1. Final position vector (after 5.00 s):
We start with the initial position vector of 31.5 m at an angle of 95.0° counterclockwise from the x-axis. To find the final position vector, we need to add the displacement vector to the initial position vector.

The displacement vector is given by:
displacement = initial velocity * time + 1/2 * acceleration * time^2

The initial velocity vector is given by:
initial velocity = velocity * cos(theta)

where velocity is 4.29 m/s and theta is 40.0°.

The acceleration vector is given by:
acceleration = acceleration * cos(theta_acceleration)

where acceleration is 1.82 m/s^2 and theta_acceleration is 200°.

Now we can calculate the displacement vector and add it to the initial position vector to find the final position vector.

2. Final velocity vector (after 5.00 s):
To find the final velocity vector, we need to add the initial velocity vector and the acceleration vector multiplied by time.

final velocity = initial velocity + acceleration * time

where initial velocity is the same as before and time is 5.00 s.

3. Magnitude of the final velocity (after 5.00 s):
Once we have the final velocity vector, we can find its magnitude by taking its absolute value or magnitude.

magnitude of the final velocity = |final velocity|

4. Direction of the final velocity (after 5.00 s):
To find the direction of the final velocity, we can use the inverse tangent function to find the angle between the final velocity vector and the x-axis.

direction of the final velocity = arctan(y_component / x_component)

where y_component and x_component are the y and x components of the final velocity vector respectively.

By following these steps, we can calculate the final position vector, final velocity vector, magnitude of the final velocity, and direction of the final velocity after 5.00 seconds.