A rocket moves straight upward, starting from rest with an acceleration of +25.5 m/s2. It runs out of fuel at the end of 4.26 s and continues to coast upward, reaching a maximum height before falling back to Earth.

Question

A rocket moves straight upward, starting from rest with an acceleration of +25.5 m/s2. It runs out of fuel at the end of 4.26 s and continues to coast upward, reaching a maximum height before falling back to Earth. 
(a) Find the rocket's velocity and position at the end of 4.26 s.
vb =	  m/s
yb =	  m

(b) Find the maximum height the rocket reaches. 
  m

(c) Find the velocity the instant before the rocket crashes on the ground. 
  m/s

Henry · Answer

a. Vf=at=25.5 m/s^2 * 4.26s=10=108.6m/s
h=0.5a*t^2 = 0.5*25.5*(4.26)^2=231.4 m

b. hmax = (Vf^2-Vo^2) / 2g,
hmax = (0-(108.6)^2)/ -19.6 = 601.7 m.

c. Vf^2 = Vo^2 + 2g*d ,
Vf^3 = 0 + 19.6*601.7 = 11793.3,
Vf = 108.6.