4. 2D Kinematics

Kinematics in 2D

Multiple Choice
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?
Multiple Choice
Bob throws a ball from his second story window to his friend Steve who is on the ground below. Assume that Bob throws the ball horizontally at $10 m / s$ , and Steve will catch the ball at a point $4.5 m$ below Bob. How far from the base of the building should Steve stand in order to catch the ball?
Multiple Choice
Jim pushes a penny off a $0.86 m$ tall table. Assume the penny is moving horizontally as it leaves the table at 5 m/s. How long is the penny in the air? Ignore air resistance.
Multiple Choice
A baseball player hits a pop fly ball. If the ball leaves the bat at $45 m / s$ at an angle of 68° above the horizontal, what is the maximum height, above the point of contact with the bat, that the ball will reach? Ignore air resistance.
Open Question
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?
Open Question
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. (a) If the mission fails, how many hours is it until the asteroid impacts the earth?
Open Question
(II) At t = 0, a particle starts from rest at 𝓍 = 0 , y = 0 and moves in the xy plane with an acceleration a (→ above a) = (4.0 î + 3.0 ĵ ) m/s². Determine
(b) the speed of the particle as a function of time,
Open Question
(II) A skier is accelerating down a 30.0° hill at 1.80 m/s² (Fig. 3–42). (b) 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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Open Question
A batter hits a fly ball which leaves the bat 0.90 m above the ground at an angle of 64° with an initial speed of 28 m/s heading toward centerfield. Ignore air resistance.
(b) The ball is caught by the centerfielder who, starting at a distance of 105 m from home plate just as the ball was hit, runs straight toward home plate at a constant speed and makes the catch at ground level. Find his speed.
Open Question
"(II) Two masses are connected by a string as shown in Fig. 8–35. Mass m_A = 3.5 kg rests on a frictionless inclined plane, while m_B = 5.0 kg is initially held at a height of h = 0.75 m above the floor.
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(b) If the masses were initially at rest, use the kinematic equations (Eqs. 2–12) to find their velocity just before m_B hits the floor. "