A toy rocket is launched vertically from ground level at time t = 0 s.The rocket engine provides constant upward acceleration during the burn phase.At the instant of engine burnout,the rocket has risen to 49.0 m and acquired an upward velocity of 60.0 m/s. The rocket continues to rise with insignificant air resistance in unpowered flight,reaches maximum height,and falls back to the ground.The maximum height reached by the rocket is closest to
A)233 m.
B)221 m.
C)209 m.
D)244 m.
E)256 m.

Question

Quizplus · Accepted Answer

The maximum height can be found using the formula $h = h_0 + v_0t + \frac{1}{2}gt^2$, where $h_0$ is the initial height, $v_0$ is the initial velocity, $g$ is the acceleration due to gravity (approximately -9.8 m/s$^2$), and $t$ is the time. However, since we are looking for the maximum height, we can use the energy conservation principle or the formula derived from it for objects under gravitational influence: $h = h_0 + \frac{v_0^2}{2g}$. Given $h_0 = 49.0$ m, $v_0 = 60.0$ m/s, and $g = 9.8$ m/s$^2$, substituting these values gives $h = 49.0 + \frac{60.0^2}{2 \times 9.8} \approx 233$ m.

A Toy Rocket Is Launched Vertically from Ground Level at Time