Starting from a location with position vector r1x = -18.3 m and r1.y = average velocity Vav.x = -2.47 m/s and vavy = 1.73 m/s. Find the components of the position vector of the rabbit's final location, r2.x and r2.y. 21.7 m, a rabbit hops around for 13.7 seconds with
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- From the origin, a particle starts at t = 0 s with a velocity vecv=7.0hatim/s and moves in the xy plane with a constant acceleration of a=(-9.0hati+3.0hatj)m/s^(2). At the time the particle reaches the maximum x coordinate, what is its (a) velocity and (b) position vector?You have a remote-controlled car that has been programmed to have velocity v = (−3t i + 2t^2 j ) m/s, where t is in s. At t = 0 s, the car is at r = (−3 i+ 2 j) m. • What is the x component of the car's position vector at 10 s? • What is the y component of the car's position vector at 10 s? • What is the x component of the car's acceleration vector at 10 s? • What is the y component of the car's acceleration vector at 10 s?A particle has a position vector given by r(t)=30 t i + (40t-tt^2) i, where r(t) is in meters and t is in seconds. Find the instantaneous velocity and instantaneous acceleration vectors as a function of time.
- A particle moving in the xy-plane has velocity V = ((2t) ?i+ (3 − t2 ) j)?/?, where t is in s. • What is the x component of the particle's acceleration vector at t = 4 s? • What is the y component of the particle's acceleration vector at t = 4 s?A zombie wolverine is launched with an initial speed v i =37.0 m/s at an initial angle theta i =53.1^ (a) Find the wolverine's position (horizontal and vertical) when t = 2.00s (b) Find the magnitude and direction of the wolverine's velocity when t = 2.00 s. (c) Find the time when the wolverine reaches the highest point of its flight, and find its height h at that point . (d) Find the horizontal range R (the horizontal distance from the starting point to the point where the wolverine hits the ground ).A fish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (12.0 î − 2.60 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (25.0 î − 1.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = ay = (b) What is the direction of its acceleration with respect to unit vector î? Draw coordinate axes on a separate piece of paper, and then add the acceleration vector with its tail at the origin. Write the numerical values for the x and y components and then use this drawing to determine the angle.° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 28.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axis
- Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = eti + sin2tj + cos3k, v(0) = i r(0) = jA Snowmobile is originally at the point with position vector 29.0m at 95 (Degrees) counterclockwise from the x-axis, moving with velocity 4.5 m/s at 40 (Degrees). It moves with constant acceleration 1.9 m/s^2 at 200 (dregrees). After 5 seconds have elapsed, find... a) Its Velocity? b) Its Position Vector?The acceleration of a particle is a = (5.00 i - 7.00 j) m/s^2. At t = 0, the particle leavesthe origin with an initial velocity v0 = (4.00 i + 1.00 j) m/s. (a) What is the y-coordinate of the particle when its x-coordinate reaches 2.00 m? (b) What are the magnitude and direction of the particle's velocity when its x-coordinate reaches 2.00 m? Draw this velocity vector.
- A basketball player is standing on the floor 10.0 m from the basket as in Figure P3.47. The height of the basket is 3.05 m, and he shoots the ball at a 40.0 angle with the horizontal from a height of 2.00 m. (a) What is the acceleration of the basketball at the highest point in its trajectory? (b) At what speed must the player throw the basketball so that the ball goes through the hoop without striking the backboard?The position r→ of a particle moving in an xy plane is given by r→=(3.00t^3−7.00t)i^+(6.00−2.00t^4)j^ with r→ in meters and t in seconds. In unit-vector notation, calculate(a)r→, (b)v→, and (c)a→ for t = 2.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 2.00 s? Give your answer in the range of (-180o; 180o).what is the x component of the particle's acceleration vector at t = 6s? what is the y component of the particle's acceleration vector at t = 6s?