Which of these is not an equation
1 answer:
You might be interested in
Let denote the rocket's position, velocity, and acceleration vectors at time
.
We're given its initial position
and velocity
Immediately after launch, the rocket is subject to gravity, so its acceleration is
where .
a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,
(the integral of 0 is a constant, but it ultimately doesn't matter in this case)
and
b. The rocket stays in the air for as long as it takes until , where
is the
-component of the position vector.
The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):
c. The rocket reaches its maximum height when its vertical velocity (the -component) is 0, at which point we have
In order to find the equivalent expression, let's use the following property:
In other words, when subtracting a negative number, we can just add the corresponding positive number, that is, switch the two negative signs for a positive sign.
So we have that:
Therefore the correct option is D.