Question

A small rocket is launched vertically from the ground and experiences an upward acceleration of 5 m/s2. The engine burns out after 4 seconds and the rocket moves under the influence of gravity until it returns to the ground. You may neglect air resistance. Draw the position, velocity, and acceleration vs. time curves for the entire flight from t=0 to t=9.5 s. Take the +y axis to be upward.

A) what is the Position vs. Time graph?

B) What is the velocity vs time graph?

Answer 1

given upward acceleration of the rocket a = 5 m/s/s

burnout time t = 4 s

a. for position vs time graph

0 < t < 4 s

h = 0.5*a*t^2 = 2.5t^2

4 < t < 9.5 s

h = 2.5*4^2 + (a*(4)*(t - 4)) - 0.5*g*(t - 4)^2

h = 40 + 20t- 80 - 4.9t^2 - 78.4 + 39.2t

h = -4.9t^2 + 59.2t -118.4

for dh/dt = 0

-9.8t + 59.2 = 0

t = 6.040816326 s

h at this point = 59.4081632 m

final h = 1.775 m

b. for velocity time graph

0 < t < 4 s

v = at = 5t

4 < t < 9.5 s

v = 5*4 - g*(t - 4) = 20 - 9.81t + 39.24

v = 59.24 - 9.81t