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A rhinoceros is at the origin of coordinates at time t1 = 0. For the time interval from t1 = 0 to t2 = 12.0 s, the rhino’s average velocity has x-component - 3.8 m/s and y-component 4.9 m/s. At time t2 = 12.0 s, (a) what are the x- and y-coordinates of the rhino? (b) How far is the rhino from the origin?

Respuesta :

Answer:

a) [tex](x_2,y_2)=(-45.6,58.8)[/tex]

b) [tex]s=74.4097\ m[/tex]

Explanation:

Given:

  • x-component of avg. velocity, [tex]v_x=-3.8\ m.s^{-1}[/tex]
  • x-component of avg. velocity, [tex]v_y=4.9\ m.s^{-1}[/tex]
  • initial position of rhino, [tex](x_1,y_1)=(0,0)[/tex]
  • initial time, [tex]t_1=0\ s[/tex]
  • final time, [tex]t_2=12\ s[/tex]

a)

As we know that average velocity is total displacement per unit time.

Position of x-coordinate of rhino:

[tex]v_x=\frac{x_2}{t_2}[/tex]

[tex]-3.8=\frac{x_2}{12}[/tex]

[tex]x_2=-45.6\ m[/tex]

Position of y-coordinate of rhino:

[tex]v_y=\frac{y_2}{t_2}[/tex]

[tex]4.9=\frac{y_2}{12}[/tex]

[tex]y_2=58.8\ m[/tex]

b)

Now the distance from the origin:

[tex]s=\sqrt{x_2^2+y_2^2}[/tex]

[tex]s=\sqrt{(-45.6)^2+(58.8)^2}[/tex]

[tex]s=74.4097\ m[/tex]

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