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.

(a) its velocity vector
(b) its position vector

s. velocity=acceleration*time

= (1.82@200)*5=91@200

Now, for position
position=origposit+vi*t+1/2 a t^2
= compute each individually, then convert to x,y coordinates, then add x,y separately.

To find the velocity vector and position vector of the snowmobile after 5.00 seconds, we need to break down the given information and apply the appropriate formulas for displacement, velocity, and acceleration.

Let's start by converting the information into vector form.

The initial position vector of the snowmobile is given as r₀ = 31.5 m at 95.0° counterclockwise from the x-axis. To convert this to a vector form, we can use the components:

r₀ = 31.5 cos(95.0°) î + 31.5 sin(95.0°) ĵ

The initial velocity vector of the snowmobile is given as v₀ = 4.29 m/s at 40.0°. We can convert this to a vector form as well:

v₀ = 4.29 cos(40.0°) î + 4.29 sin(40.0°) ĵ

The constant acceleration of the snowmobile is given as a = 1.82 m/s² at 200°. Again, let's convert this to a vector form:

a = 1.82 cos(200°) î + 1.82 sin(200°) ĵ

Now that we have the vectors, we can apply the kinematic equations to find the velocity vector and position vector after 5.00 seconds:

(a) Velocity vector after 5.00 seconds:
To find the velocity vector v at a given time t, we can use the formula:

v = v₀ + a * t

Substituting the values, we have:

v = (4.29 cos(40.0°) î + 4.29 sin(40.0°) ĵ) + (1.82 cos(200°) î + 1.82 sin(200°) ĵ) * 5.00

Calculating the values, we get:

v = (4.29 cos(40.0°) + 1.82 cos(200°) * 5.00) î + (4.29 sin(40.0°) + 1.82 sin(200°) * 5.00) ĵ

Calculate the values using a scientific calculator or software, and you will have the velocity vector after 5.00 seconds.

(b) Position vector after 5.00 seconds:
To find the position vector r at a given time t, we can use the formula:

r = r₀ + v₀ * t + (1/2) * a * t²

Substituting the values, we have:

r = (31.5 cos(95.0°) î + 31.5 sin(95.0°) ĵ) + (4.29 cos(40.0°) î + 4.29 sin(40.0°) ĵ) * 5.00 + (1/2) * (1.82 cos(200°) î + 1.82 sin(200°) ĵ) * (5.00)²

Calculating the values, we get:

r = (31.5 cos(95.0°) + 4.29 cos(40.0°) * 5.00 + (1/2) * 1.82 cos(200°) * 5.00²) î + (31.5 sin(95.0°) + 4.29 sin(40.0°) * 5.00 + (1/2) * 1.82 sin(200°) * 5.00²) ĵ

Calculate the values using a scientific calculator or software, and you will have the position vector after 5.00 seconds.