Calculate the centre of mass of the object shown below

[LadyTwi]

I have a few questions that are driving me nuts.

First: Calculate the centre of mass of the object shown below. Assume that the mass density is uniform. Place the origin, O, at the lower left. If the positive x-axis points to the right along the page, what is the x coordinate of the centre of mass, in terms of a? If the positive y-axis points up along the page, what is the y coordinate of the centre of mass, in terms of a?

http://www.learning.physics.dal.ca/dalphysicslib/Graphics/Gtype15/CentreOfMass4.gif

So, this object could be broken up into four squares right? Would finding the center of mass of each square help?

Second: A 7490 kg rocket is set for vertical firing from the Earth's surface. If the exhaust speed is 1550 m/s, how much gas must be ejected each second in order for the thrust to be equal to the weight of the rocket? How much gas must be ejected each second to give the rocket an initial upward acceleration of 16 m/s2?

I already found how much gas must be ejected for the thrust to equal the weight of the rocket: 47.36 kg

I'm unsure of how to relate the acceleration to the problem. It's probably so obvious. XD

 

[ehild]

So, this object could be broken up into four squares right? Would finding the center of mass of each square help?

Yes, it will help.

How much gas must be ejected each second to give the rocket an initial upward acceleration of 16 m/s2?

I already found how much gas must be ejected for the thrust to equal the weight of the rocket: 47.36 kg

I'm unsure of how to relate the acceleration to the problem. It's probably so obvious.

Use: F=ma. F is the resultant of the thrust (upward) and gravity (downward). You can calculate the thrust and then the mass of gas from it.

ehild

 

[LadyTwi]

All right, I got both answers. Thanks!