CAS PY 212 Lecture 2: Motion w/ constant acceleration : 2D

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byzantiumeagle450

27 Mar 2018

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V = vo + at xo is the initial starting position. A is the initial velocity is the constant acceleration. Galileo "s observations two objects dropped at the same time win take the same amount of time to fall ( this is. A rock is released from rest at the top of a zom tall building . (a) How long does the rock take to fall to the ground ? ( b ) what is its impact velocity g =

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A student stands at the edge of a cliff and throws a stonehorizontally over the edge with a speed of vi = 18.2 m/s. The cliffis h = 49.5 m above a body of water as shown in the figurebelow.

(a) What are the coordinates of the initial position of the stone?(Do not assume that the student is the point of origin.)

(b) What are the components of the initial velocity of thestone?

(c) What is the appropriate analysis model for the vertical motionof the stone? (Select all that apply.)
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constant velocity motion free fall motion g = 9.8 m/s2 noacceleration from gravity g = -9.8 m/s2

(d) What is the appropriate analysis model for the horizontalmotion of the stone? (Select all that apply.)
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constant velocity in the horizontal direction g = 9.8 m/s2 g = -9.8m/s2 free fall motion no acceleration from gravity

(e) Write symbolic equations for the x and y components of thevelocity of the stone as a function of time. (Use the following asnecessary: vix, g, and t.)

(f) Write symbolic equations for the position of the stone as afunction of time. (Use the following as necessary: vix, g andt.)

(g) How long after being released does the stone strike the waterbelow the cliff?

(h) With what speed and angle of impact does the stone land?

The figure shows three graphs, A, B, C, which collectively describe the motion of an object in one dimension. The horizontal axis of each graph is time (symbol t). The vertical axes of the graphs are different. For one graph the vertical axis is position (symbol x), for another, it is the velocity (symbol v), and for another, it is acceleration (symbol a). Where the axes across is the point of zero for both time and the quantity corresponding to the vertical axis. Part A: For which sequence of graphs is the vertical coordinate position, velocity, and acceleration, respectively? (e.g., If you think graph Y is position versus time, graph X is velocity versus time, and graph Z is acceleration versus time, then your answer is Y, X, Z.). Multiple choice: 1)C, A, B 2)A, C, B 3)C, B, A 4)B, C, A 5)B, A, C 6)A, B, C. Part (b) Which one of the following situations can be most accurately represented by the graph, consistent with your answer to part (a)? (1) A car driving in the negative x-direction suddenly shifts into reverse and, with tires spinning, slows to a momentary stop before beginning to move in the position x-direction. (2)A car driving in the position x-direction slams on its brakes and comes to rest. (3) A rock is dropped from the rest from the top of a tall building. Assume air drag can be neglected, in which case its speed increases by the same amount each second. Take upward to be the position x-direction. (4) A sprinter runs a 100-meter dash and she runs in the negative x-direction. Starting from rest, she has a constant acceleration for the first 50 meters, then a constant speed for the remaining 50. Multiple choices: 1)4, 2)3, 3)2, 4)1.

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If a projectile is fired with an initial velocity of v0 meters per second at an angle a above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x=(v₀cos α)t, y=(v₀sin α)t−1/2gt² where g is the acceleration due to gravity (9.8 m/s^2). If a gun is fired with α=30° and v₀=500 m/s, when will the bullet hit the ground? How far from the gun will it hit the ground? What is the maximum height reached by the bullet?

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CAS PY 212 Lecture 2: Motion w/ constant acceleration : 2D

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