A rocket experiences a constant force even as the amount of fuel in its fuel tanks decreases. What happens to the acceleration o
2 answers:
We can answer this question by looking at Newton's second law:
which can be rewritten as
where F is the force experienced by the rocket, m is its mass, a is its acceleration. In the rocket's case, the mass of the rocket decreases (because the fuel in the tank decreases), while the force remains constant, so the ratio F/m increases, and therefore the acceleration of the rocket increases.
Therefore, the correct answer is
D - The acceleration increases because the mass decreases.
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First compute the resultant force F:
Then use Newton's second law to determine the acceleration vector for the particle:
Let and
denote the particle's position and velocity vectors, respectively.
(a) Use the fundamental theorem of calculus. The particle starts at rest, so . Then the particle's velocity vector at <em>t</em> = 10.4 s is
If you don't know calculus, then just use the formula,
So, for instance, the velocity vector at <em>t</em> = 10.4 s has <em>x</em>-component
(b) Compute the angle for
:
so that the particle is moving at an angle of about 313º counterclockwise from the positive <em>x</em> axis.
(c) We can find the velocity at any time <em>t</em> by generalizing the integral in part (a):
Then using the fundamental theorem of calculus again, we have
where is the particle's initial position. So we get
So over the first 10.4 s, the particle is displaced by the vector
or a net distance of about 395 m away from its starting position, in the same direction as found in part (b).
(d) See part (c).