4. 2D Kinematics

A survey drone has just completed a scan at x,y coordinates (57m, 8m) at t=0. It needs to return to a lab located at (-115, 72) m. If its initial velocity is 16m/s in the +y-direction, and it has only 18s of battery life remaining, what constant acceleration (magnitude and direction) does it need to reach the lab?

A 4.0 x 10¹⁰ 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 10⁹ N of thrust. The rocket is fired when the asteroid is 4.0 x 10⁶ km away from earth. You can ignore the earth's gravitational force on the asteroid and their rotation about the sun.The radius of the earth is 6400 km. By what minimum angle must the asteroid be deflected to just miss the earth?

A 4.0 x 10¹⁰ 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 10⁹ N of thrust. The rocket is fired when the asteroid is 4.0 x 10⁶ km away from earth. You can ignore the earth's gravitational force on the asteroid and their rotation about the sun. If the mission fails, how many hours is it until the asteroid impacts the earth?

(II) At t = 0, a particle starts from rest at 𝓍 = 0, y = 0 and moves in the xy plane with an acceleration $\overrightarrow{a}$ = (4.0 î + 3.0 ĵ ) m/s². Determine the speed of the particle as a function of time.

A skier is accelerating down a 30.0° hill at 1.80 m/s² (Fig. 3–42). How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 125 m? 

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