Question

A rocket toy moves vertically up with a constant acceleration a = 20 ms2. After some time, its fuel gets exhausted and then it falls under gravity . If maximum height attained by the rocket is 120 m, then speed of rocket when fuel is just exhausted (g = 10 m/s2)

Answer 1

acceleration of rocket in upward direction, a = 20 m/s²

Let velocity of rocket when fuel gets exhausted be v m/s

using formula, v = u + at

as initial velocity, u = 0

then, v = at .....(1)

distance travelled by rocket with acceleration a = 20m/s² is s = 1/2at²

and distance travelled by rocket in gravity , S ; 0² = v² + 2(-g)S

or, S = v²/2g

from equation (1),

S = at²/2g

so, s + S = 1/2 at² + a²t²/2g =120

or, 1/2 × 20 × t² + 400t²/20 = 120

or, 30t² = 120 => t = 2s

now, speed of rocket when fuel is exhausted, v = at = 20 × 2 = 40m/s