Question

A rocket accelerates upward from rest at a rate of 5 m/s2. At a height of 1000m, the engines burn out and it coasts the rest of the way with an acceleration of -9.8 m/s2.

a) What is the rocket's velocity at burnout (h=1000m) in meters/second?

b) For how many seconds did the rocket engine burn?

c) What is the rocket's maximum altitude?

Answer 1

here,

the initial acceleration of rocket , a = 5 m/s^2

a)

at h1 = 1000 m

the velocity of rocket , v = sqrt(2 * a * h1)

v = sqrt(2 * 5 * 1000) = 100 m/s

b)

let the time interval for which the rocket engine burn be t1

using first equation of motion

v = u + a * t1

100 = 0 + 5 * t1

t1 = 20 s

the rocket will burn for 20 s

c)

the rocket maximum altitude , h = h1 + v^2 /2g

h = 1000 + 100^2 /(2 * 9.81) m

h = 1510 m