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 64 m and acquired an upward velocity of $ 60 \mathrm{~m} / \mathrm{s} $ The rocket continues to rise with insignificant air resistance in unpowered flight, reaches maximum height, and falls back to the ground. The time interval during which the rocket engine provided the upward acceleration, is closest to
A) 2.1 s.
B) 2.3 s.
C) 1.9 s.
D) 1.7 s.
E) 1.5 s.

Question

Quizplus · Accepted Answer

The correct answer is A.The rocket's initial velocity is 0 m/s, and its final velocity at burnout is 60 m/s. The acceleration during the burn phase is:$$a = \frac{v_f - v_i}{t} = \frac{60 \mathrm{~m} / \mathrm{s} - 0 \mathrm{~m} / \mathrm{s}}{t}$$The rocket rises to a height of 64 m during the burn phase, so:$$d = v_i t + \frac{1}{2} a t^2 = 0 \mathrm{~m} + \frac{1}{2} a t^2$$Solving for t, we get:$$t = \sqrt{\frac{2d}{a}} = \sqrt{\frac{2(64 \mathrm{~m})}{a}}$$Substituting the expression for a, we get:$$t = \sqrt{\frac{2(64 \mathrm{~m})}{\frac{60 \mathrm{~m} / \mathrm{s} - 0 \mathrm{~m} / \mathrm{s}}{t}}}$$Solving for t, we get:$$t = 2.1 \mathrm{~s}$$

A Toy Rocket Is Launched Vertically from Ground Level at Time