A toy rocket is launched vertically from ground level at time t = 0.00 s.The rocket engine provides constant upward acceleration during the burn phase.At the instant of engine burnout,the rocket has risen to 81 m and acquired an upward velocity of 40 m/s.The rocket continues to rise with insignificant air resistance in unpowered flight,reaches maximum height,and falls back to the ground.The upward acceleration of the rocket during the burn phase is closest to
A)9.9 m/ $\mathrm { s ^2}$
B)9.6 m/ $$\mathrm { s }^2$$
C)9.3 m/ $$\mathrm { s }^2$$
D)9.0 m/ $\mathrm { s }^2$
E)8.7 m/ $\mathrm { s }^2$

Question

Quizplus · Accepted Answer

Let's start by using the kinematic equations for motion with constant acceleration. We'll take upward as positive.

During the burn phase:

Initial velocity, u = 0 
Final velocity, v = 40 m/s 
Displacement, s = 81 m 
Time, t = ?

We know that acceleration, a, is constant during the burn phase.

From the third kinematic equation:

v^2 = u^2 + 2as

40^2 = 2a(81)

a = 9.9 m/s^2

Therefore, the upward acceleration of the rocket during the burn phase is 9.9 m/s^2, which is closest to choice A).

A Toy Rocket Is Launched Vertically from Ground Level at Time