A $20,000$ kg rocket has a rocket motor that generates $3.0\times {10}^{5}N$ of thrust. Assume no air resistance.

a. What is the rocket’s initial upward acceleration?

b. At an altitude of $5000$ m the rocket’s acceleration has increased to $6.0m/s^2$ . What mass of fuel has it burned?

Acceleration, charge at which speed modifications with time, in phrases of each velocity and course. A factor or an item transferring in a immediately line is extended if it hastens or slows down. Motion on a circle is extended even though the velocity is constant, due to the fact the course is usually changing.

We are given:

$$\begin{gathered} m=2000kg \\ F=3.{10}^{5}N \\ h=5km=5000m \\ {a}_2=6m/s^2 \end{gathered}$$

Here, $m$is the mass, $F$is the gravitational force, $h$is the height, $a$is the acceleration

According to the newton second law:

$$\begin{gathered} F-mg=ma \\ a=\frac{F-mg}{m} \\ a=\frac{3.{10}^{5}N-20,000kg\times 9.81m/s^2}{20,000kg} \\ a=5.19m/s^2 \end{gathered}$$

When rocket moves it loses its mass such motion is called the motion of the body of variable mass.

$$\begin{gathered} F=ma \\ F-m_{2}g=m_2{a}_2 \\ {m}_2=\frac{F}{a_2+g} \\ {m}_2=\frac{3.{10}^{5}N}{6m/s^2+9.81m/s^2} \\ {m}_2=18975.33kg \end{gathered}$$

The mass that the rocket loss $m_3$will be the difference between the initial mass$m$ and the mass at the time$m_2$

$t+△t$

$$\begin{gathered} m_3=m-m_2 \\ {m}_3=20000kg-18975.33kg \\ {m}_3=1024.67kg \end{gathered}$$