Question

a 540 kg satellite moves through deep space with a speed of 27m/s. a booster rocket on the satellite fir 1.4 s, giving the force to the satellite the speed if the rocket increase to 31 m/s calculate the force given by the booster rocket to the satellite

Answer 1

Force = 1544.4N

Step-by-step explanation:

In physics, acceleration can be defined as the rate of change of the velocity of an object with respect to time.

This simply means that, acceleration is given by the subtraction of initial velocity from the final velocity all over time.

Hence, if we subtract the initial velocity from the final velocity and divide that by the time, we can calculate an object’s acceleration.

Mathematically, acceleration is given by the equation;

`Acceleration (a) = (final \; velocity - initial \; velocity)/(time)`

`a = (v - u)/(t)`

Where;

• a is acceleration measured in
  `ms^(-2)`

• v and u is final and initial velocity respectively, measured in
  `ms^(-1)`

• t is time measured in seconds.

Given the following data;

Mass, m = 540kg

Initial velocity, u = 27m/s

Final velocity, v = 31m/s

Time, t = 1.4 secs

To find the acceleration:

`a = (31 - 27)/(1.4)`

`a = (4)/(1.4)`

Acceleration, a = 2.86m/s²

Now to find the Force;

Force is given by the multiplication of mass and acceleration.

Mathematically, Force is;

`F = ma`

Where;

• F represents force measured in Newton.

• m represents the mass of an object measured in kilograms.

• a represents acceleration measured in meter per seconds square.

Substituting into the equation, we have;

`F = 540*2.86`

Force = 1544.4N

Therefore, the force given by the booster rocket to the satellite is 1544.4 Newton.