Question

Question No. 3

A robotic vehicle, is exploring the surface of Mars. The landing craft is the origin of coordinates, and the surrounding Martian surface lies in the x-y plane. The rover, which we represent as a point, has x-and y-coordinates that vary with time:

x = 2.0m − (0.25 m/s^2)t^2

y = (1.0m/s)t + (0.25 m/s^3)t^3

(a)Find the rover’s coordinates and its distance from the lander at t = 2.0 s.

(b)Find the rover’s displacement and average velocity vector during the interval

from t = 0.0 s to t = 2.0 s.

(c) Derive a general expression for the rover’s instantaneous velocity vector.

Express the instantaneous velocity at t = 2s in component form an also in term of magnitude and direction

Question No. 5

Vectors A and B lie in an xy plane. A has magnitude 8.00 and angle 130°; has components Bx = -7.72 and By = -9.20. What are the angles between the negative direction of the y axis and (a) the direction of A , (b) the direction of the product A × B , and (c) the direction of A × (B + 3k̂)?

Answer 1

3) a)

$$x=2-0.25(2)^2=1.0\ m\\y=(1)2+0.25(2)^3=4.0\ m\\s=\sqrt{(1-2)^2+4^2}=4.1\ m$$

b)

$$\vec{s}=\vec{r}-\vec{r_0}=(1-2,4-0)=(-1,4)\ m\\\vec{v}=\frac{1}{2}(-1,4)=(-0.5,2)\frac{m}{s}$$

c)

$$v_x=-0.5t,v_y=1-0.75t^2\\\vec{v}(2)=(-1,-2)\frac{m}{s}$$

Magnitude:

$$2.24\frac{m}{s}$$

Direction:

$$\theta=-117\degree$$

5) a)

$$\theta=270-130=140\degree$$

b)

$$\theta=90\degree$$

c)

$$\theta=90\degree$$