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

We can use the equation for the maximum height reached by the rocket, which is given by:

h_max = (v^2)/(2g) + R

where:
- v is the initial velocity of the rocket
- g is the acceleration due to gravity
- R is the radius of the earth

Substituting the given values, we get:

h_max = (9100^2)/(2*9.8) + 6371000
h_max = 1.26e+07 meters

Therefore, the maximum height reached by the rocket is 1.26e+07 meters, which is answer choice D.

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