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Suppose a rocket which starts from rest fall in constant gravitational feild
Suppose a rocket which starts from rest fall in constant gravitational feild.At the instant it start to fall and eject gas at constant rate in the direction of gravitational feild at speed v0 with respect to rocket. find the speed after time t and how far does the rocket in time t ?
Expert Solution
The speed after time t can be expressed by the equation vf = 9.81t.
The distance of the rocket after time t is d = 4.905t2.
Explanation
Using kinematic equation to find the final velocity given the acceleration and initial velocity:
vf = vo + at
where:
vf = final velocity (m/s)
vo = initial velocity (m/s)
a = acceleration (m/s2)
t = time (s)
The rocket starts from rest so that vo = 0 m/s. And since this is a case of a free fall, we will be using a = +9.81 m/s2. Therefore, the speed after time t is:
vf = vo + at
vf = 0 + 9.81t
vf = 9.81t
Another kinematic equation that we can use to find the distance after time t is:
d = vot + 0.5at2
where:
d = distance (m)
vo = initial speed (m/s)
t = time (s)
a = acceleration (m/s2)
Using again a = +9.81 m/s2 as the acceleration and vo = 0 m/s, the equation to find the distance of the rocket after time t is:
d = vot + 0.5at2
d = 0t + 0.5(9.81)t2
d = 4.905t2
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