Suppose a rocket is fired upward from the surface of the earth with an initial velocity (measured in m/s). Then the maximum height (in meters) reached by the rocket is given by the function where the radius of the earth is meters and the acceleration due to gravity is 9.8 . If the initial velocity of the rocket is 9100 m/s what is the maximum height reached by the rocket?
A) meters
B) 5.26e+14 meters
C) -7.86e+07 meters
D) 1.26e+07 meters
E) 6.35 meters

Question

Suppose a rocket is fired upward from the surface of the earth with an initial velocity  (measured in m/s). Then the maximum height  (in meters) reached by the rocket is given by the function  where the radius of the earth  is  meters and the acceleration due to gravity  is 9.8  . If the initial velocity of the rocket is 9100 m/s what is the maximum height reached by the rocket?
A) meters 
B) 5.26e+14 meters 
C) -7.86e+07 meters 
D) 1.26e+07 meters 
E) 6.35 meters

Quizplus · Accepted Answer

Using the kinematic equation: $h=\frac{v_0^2}{2g}+\frac{v_0^2}{2g}-\frac{2GM}{R+H}$, where $h$ is the maximum height reached by the rocket, $v_0$ is the initial velocity of the rocket, $g$ is the acceleration due to gravity, $G$ is the gravitational constant, $M$ is the mass of the earth and $R$ is the radius of the earth.

Plugging in the given values, we get:

$h = \frac{9100^2}{2	imes 9.8} + \frac{9100^2}{2	imes 9.8} - \frac{2 	imes 6.674	imes 10^{-11} 	imes 5.972	imes 10^{24}}{6.371	imes 10^6 + h}$

$h = 1.26	imes 10^7$ meters.

Therefore, the rocket reaches a maximum height of 1.26e+07 meters, which is option D.

Suppose a Rocket Is Fired Upward from the Surface of the Earth