A 4.0 x 10^10 kg asteroid is heading directly toward the center of the earth at a steady 20 km/s. To save the planet, astronauts strap a giant rocket to the asteroid perpendicular to its direction of travel. The rocket generates 5.0 x 10^9 N of thrust. The rocket is fired when the asteroid is 4.0 x 10^6 km away from earth. You can ignore the earth's gravitational force on the asteroid and their rotation about the sun.(b) The radius of the earth is 6400 km. By what minimum angle must the asteroid be deflected to just miss the earth?

Video transcript

Hey, everyone. Today, we're being told that to physics enthusiasts devise an experiment in this experiment, a remote controlled rocket is attached to a ball which is perpendicular to his direction of travel That is then dropped from a height of three km, ignoring the gravitational pull of the Earth on the ball. We're being asked to determine the minimum angle at which the ball must be deflected in order to miss the massive circular orbit of 0.8 km exactly beneath it. So let's think about this. We have and let's just draw this out real quick. Let's just say we have um we have a little rocket ship, rocket ship. This is a very bad rocket ship. I apologize. We have our little rocket ship, right? And we have a ball, let's say this is the direction of travel. We have a ball that is being dropped directly towards the ground below. Now, the ground, as it's mentioned in the problem, let's just say that the sphere has a radius, is it radius Of 0.8 km? And we're being told that the ball itself is dropping three km has dropped from a height of 3km. So with this, we're being asked to find if we make this a little right triangle. As one, does we make this a little right triangle? We're being asked to find, what is the minimum angle that the ball must be deflected in order to miss the Massive circular object, the circular object below it. So what is this angle that it must deflect to breach that 0. km meter or rather what is the angle data here? So since we have the values since this functions as a little right triangle, let me write that in green, so you can see functions like a little right triangle, right, then if we use our Trigon metric identities we have. So ah Tua 10 is equal to opposite over the adjacent in relation to the angle. So the opposite over the or let me draw that out the opposite over the adjacent to this angle here angle theta. So we could say therefore that tan theta is equal to 0.8 divided by three. Therefore, data will be equal to the inverse tangent of 0.8 over three. Calculating this, we get a final answer of 14.93°, which we can round up to 15°. So the minimum angle at which the ball must deflect in order to miss the massive circular object below it Is 15° or answer choice DI hope this helps. And I look forward to seeing you all in the next one.