A 1 kg model rocket is launched vertically from rest with a constant thrust of 20 N until the rocket reaches an altitude of 20 m. Then the thrust ends. Neglecting air resistance, find the speed of the rocket when it returns to the ground
Answers
speed of rocket when it returns to the ground is 34.64 m/s
It has given that a 1 kg model rocket is launched vertically from rest with a constant thrust of 20 N until the rocket reaches an altitude of 20 m. Then the thrust ends. (Neglecting air resistance)
we have to find speed of rocket when it returns to the ground.
first find speed of rocket when thrust ends.
net force acting on rocket before thrust ends , F = thrust - weight of rocket
= 20N - 1kg × 10m/s² = 10N
workdone on the rocket, W = net force applied on the rocket × height reached by rocket.
W = 10N × 20m = 200 J
now workdone = change in kinetic energy
⇒ 200 J = 1/2 mv² - 1/2mu²
⇒200 = 1/2 × 1kg × v² - 1/2 × 1kg × 0
⇒200 = 1/2 × v²
⇒v = 20m/s
now height covered by rocket to be rest, s = v²/2g
= 20²/2 × 10 = 40m
final height of rocket , h = 20m + 40m = 60m
now rocket falls from 60m height to the ground.
using formula, v² = u² + 2as
⇒v² = 0² + 2(-10)(-60)
⇒v² = 1200
⇒v = 20√3 = 34.64 m/s
therefore, speed of rocket when it returns to the ground is 34.64 m/s
look this carefully and try to understand .....the answer is 20√2m/s
