Physics: Aspaceship plans to land on earth. it is currently going 1000 m/s and has a mass of 500 mg. it is so close to the ground that it must stop within 10 seconds. what forced to the thrusters need to put on the spaceship

Given,The initial position of the boat, d_i=(5i-2j+4k) mThe initial velocity of the boat, u=(4i+j-3k) m/sThe time period, t=8 sThe final velocity of the boat, v=(12i-7j+13k) m/sTo find:a) The position of the object after 8 sb) The acceleration of the object.Explanation:a)From the equation of motion, the total distance traveled by the object is given by,On substituting the known values,Thus the final position of the boat is,b)The acceleration of an object is given by,On substituting the known values,Final...

Aspaceship plans to land on earth. it is currently

Ответ:

moneykingmarco079

12.11.2022

Physics

Given,

The initial position of the boat, d_i=(5i-2j+4k) m

The initial velocity of the boat, u=(4i+j-3k) m/s

The time period, t=8 s

The final velocity of the boat, v=(12i-7j+13k) m/s

To find:

a) The position of the object after 8 s

b) The acceleration of the object.

Explanation:

From the equation of motion, the total distance traveled by the object is given by,

$d=\frac{1}{2}(v+u)t$

On substituting the known values,

$\begin{gathered} d=\frac{1}{2}[(12\hat{i}-7\hat{j}+13\hat{k)}+(4\hat{i}+\hat{j}-3\hat{k})]8 \\ =4\times(16\hat{i}-6\hat{j}+10\hat{k}) \\ =(64\hat{i}-24\hat{j}+40\hat{k})\text{ m} \end{gathered}$

Thus the final position of the boat is,

$\begin{gathered} d_f=d_i+d \\ =\left(5\hat{i}-2\hat{j}+4\hat{k}\right)+(64\hat{i}-24\hat{j}+40\hat{k}) \\ =(69\hat{i}-26\hat{j}+44\hat{k})\text{ m} \end{gathered}$

The acceleration of an object is given by,

$a=\frac{v-u}{t}$

On substituting the known values,

$\begin{gathered} a=\frac{(12\hat{i}-7\hat{j}+13\hat{k)}-(4\hat{i}+\hat{j}-3\hat{k})}{8} \\ =\frac{8\hat{i}-8\hat{j}+16\hat{k}}{8} \\ =(\hat{i}-\hat{j}+2\hat{k})\text{ m/s}^2 \end{gathered}$

Final

a) Thus the position of the boat after 8 s is

$\begin{equation*} (69\hat{i}-26\hat{j}+44\hat{k})\text{ m} \end{equation*}$

The acceleration of the boat is

$\begin{equation*} (\hat{i}-\hat{j}+2\hat{k})\text{ m/s}^2 \end{equation*}$

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Aspaceship plans to land on earth. it is currently going 1000 m/s and has a mass of 500 mg. it is so close to the ground that it must stop within 10 seconds. what forced to the thrusters need to put on the spaceship

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