Physics, 28.10.2020 15:50 hanjonez

What constant acceleration is required to bring a rocket to an altitude of 650 m [up] from rest in 7.2 s? What is the rocket’s velocity at that point?

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Answer from: kingoc321

a = 15.68 [m/s²]; v = 112.92 [m/s]

Explanation:

To solve this problem we must use the combination of two interesting topics of physics, the principle of energy conservation and then the application of kinematics.

The principle of Energy Conservation tells us that kinetic energy is transformed into potential energy or vice versa. For this particular problem, we must imagine the rocket at a height above 650 [m], suddenly this rocket falls to the ground. We will propose the reference point of potential energy at ground level, at this point the potential energy is equal to zero.

$E_{pot}=E_{kin}$

$E_{pot}=m*g*h\\E_{kin}=\frac{1}{2}*m*v^{2}$

where:

m = mass of the rocket [kg]

g = gravity acceleration = 9.81[m/s²]

v = velocity of the rocket [m/s]

m*g*h = 0.5*m*v²

9.81*650 = 0.5*v²

v = √((6376.5)/0.5)

v = 112.92 [m/s]

Now using the following kinematic equation we have:

$v_{f} = v_{o} + (a*t)$

where:

Vf = final velocity = 112.92 [m/s]

Vo = initial velocity = 0 (at the begining the rocket is at rest)

a = rocket acceleration [m/s²]

t = time = 7.2 [s]

Note: in the kinematics equation the positive sign of acceleration means that the rocket accelerates in the direction of motion, i.e. activates its thrusters to descend and descend to 650 [m] in 7.2 [s].

112.92 = 0 + (a*7.2)

a = 15.68 [m/s²]

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

Answer from: Quest

i already answered it by 34/s

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What constant acceleration is required to bring a rocket to an altitude of 650 m [up] from rest in 7...