Questin on Motion in Gravitational Field

Question

I just feel like I don't fully understand the following multiple-choice question despite the fact that I got the answer (which I still don't know if it's correct or not).

"An astronaut is standing on Mars. The astronaut throws and an object of mass 0.30kg vertically up at an initial speed of 9.0m/s. It reaches a maximum height of 11 metres. What is the magnitude of acceleration of the object, given the mass and radius of Mars are 6.42*10^23 kg and 3397km respectively?"

A) 3.7 m^-2

B) 1.4 m^-2

C) 9.0 m^-2

D) 9.8 m^-2

I chose A and what I did was that I calculated the force acting on the object by Mars using GMm/r^2 then I used F=ma to figure out the acceleration. However, I just feel like I did something wrong since I ignored the force acting on the object by the astronaut when he throws it up. Also I did not touch other given numbers such as the initial speed or maximum height at all.

Could someone please shed some light on this question for me please? I just began learning this topic at school hence everything seems a bit vague to me.

Answer 1

This question provides either excess information, or not enough information, depending on how you choose to solve it

The most straight-forward way:

Of the five quantities of kinematics (initial velocity, final velocity, distance, acceleration and time) you are told three for the free flight portion of the rock's motion: initial velocity, final velocity and distance.

Therefore you can solve for the other two quantities: time (not required here) and acceleration.

More obscurely: we have that the acceleration of gravity comes from the gravitational force between the rock and the planet, so for any mass $m$ on Mars. mass $m_{Mars}$:$$mg_{Mars} = \frac{G\times m \times m_{Mars}}{r_{Mars}^2}$$so, cancelling out $m$:$$g_{Mars} = \frac{G\times m_{Mars}}{r_{Mars}^2}$$

Now, if you have the Universal Gravitational Constant memorized, you are all set.