Gn some distant dystopian future on the surface of a war ravaged mars, a rocket is launched from top of a weapons platform located 8 m above the ground at an angle of 30◦ above the horizontal and with an initial speed of 12 m/s. the rocket is equipped with a special propulsion system which provides a constant horizontal acceleration of 2 m/s2, t seconds after the rocket has been launched. assuming a constant downward acceleration of 4 m/s2 due to gravity on mars, give a vector-valued function r(t) (with a horizontal component and a vertical component) which represents the position of the rocket relative to the point on the ground directly below the launch point of the rocket t seconds after launch.

the vector position is   r = (10.4 t + t²) i + (8+ 6t - 2 t²) j

Explanation:

In this problem we have acceleration in the x and y axes, therefore we will use the accelerated motion equations

   X = Xo + Vox t + ½ aₓ t²

   Y = I + I go t + ½ t²

We calculate the components of velocity using trigonometry

   Vox = Vo cos θ = 12 cos 30

   Voy = Voy sin θ = 12 sin 30

    Vox = 10.4 m / s

    Voy = 6 m / s

The value accelerations are data

    aₓ = 2 m / s²

    = - 4 m / s²

The initial position is

    Xo = 0

    Yo = 8 m

    Since the launching point is 8 m above the ground.  The acceleration is negative because it has a downward direction; with this data we write the equations of the position

      X = 10.4 t + ½ 2 t²

      Y = 8 + 6 t - ½ 4 t²

     X = 10.4 t + t²

      Y = 8 + 6 t - 2 t²

We write the position vector

    r = x i + y j

     r = (10.4 t + t²) i + (8+ 6t - 2 t²) j

this the vector position

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles