00:01
Question 75.
00:03
It's a very long question, so i'm not going to quite read it all, but i outlined it here.
00:08
We have a rocket, or a rover, i guess, that's landing on mars, which i'm representing by this rectangle here.
00:17
So as it enters mars ' atmosphere, it enters very, very fast with this initial speed of 19 ,000, 300 kilometers.
00:25
And in various stages, deemed stage 1, stage 2, and stage 3, slowly reduces.
00:31
Its initial high velocity, finally in the 4 -2 on stage 3, a zero velocity where it will eventually land on the planet.
00:43
So our goal for each part, well, the goal for the question is to find the force exerted on the spacecraft in each of these stages.
00:51
And while their methods to slow down from their initial to final velocities are different, the idea for how each unit is solved would be the same.
01:02
So we're told initially the mass of the rocket and the acceleration due to gravity on mars, and we can use that to find the net force applied to the rocket.
01:13
I keep saying rocket, but it is just a rover.
01:16
So, yeah, so if the question did ask to drop free body diagram for each stage, really it's the same thing happening in each scenario, where the idea goal is to slow down the rocket.
01:30
The rocket's a rover, just so it lands perfectly on mars.
01:35
I'll draw one and really it's the same for each scenario.
01:39
So you know the rover has a weight pulling itself down towards the martian surface, and it is traveling downwards, so the net forces the ma down that way, and that is a counteract by the thrust of motion.
01:56
I'll just call f here, pulling the, like it's really thrusting it up to reduce the direction of the velocity.
02:04
So i want to call downward motion to be positive, my positive y, just be a little bit easier with the math.
02:11
So we need to find the overall force.
02:14
That would be equivalent to ma plus the weight of the rover.
02:18
Man, i keep saying rocket.
02:20
I'm not sure why.
02:21
I guess it has to deal with space, so i forgive me, but if i say rocket rover, i, of course, mean the same thing.
02:27
To reach the scenario, we don't have acceleration.
02:29
So during each stage, we'll solve for acceleration and use it in this equation, where we can also simplify this to be mass times the acceleration plus, plus our g prime, our new g value, since the weight is just mass times the g of the planet that we're dealing with.
02:47
And so we can find our velocity, our acceleration, just by simple kinematics.
02:55
We have, if we're traveling downwards, our velocity is positive down, positive down, but we're accelerating upwards to slow down the motion.
03:03
So that's why we have a negative sign for acceleration there.
03:06
And if you look, we are given initial velocity, final velocity, and time...