In the figure, particle A moves along the line y = 31 m with a constant velocity v of magnitude 3.0 m/s and directed parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant acceleration a of magnitude 0.42 m/s?. What angle 0 between a and the positive direction of the y axis would result in a collision? B
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- particle A moves along the line y 30 m with a constant velocity of magnitude 3.0 m/s and parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with a zero initial speed and a constant acceleration of magnitude 0.40 m/s2.What angle u between and the positive direction of the y axis would result in a collision?In the figure, particle A moves along the line y = 31 m with a constant velocity of magnitude 2.7 m/s and parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant acceleration of magnitude 0.48 m/s2. What angle ? between and the positive direction of the y axis would result in a collision?Particle A moves along the line y = 30 m with a constant velocity vector v of magnitude 3.0 m/s and parallel to the x axis. At the instant particle A passes the y axis , particle B leaves the origin with a zero initial speed and a constant acceleration vector a of magnitude 0.40 m/s2 . What angle theta between vector a and the positive direction of the y axis would result in a collision?
- Position vector of a moving particle is given by r(t)= (2t2−5t+2, 2t2+1,(t+1)2) (a) At what time(s) does the particle pass the yz -plane correctly? (b) What are the particle (i) coordinates, (ii) velocity, (iii) speed, and ((iv) acceleration at t=1 correctly?Given the displacement vector ? =[3.1?2, 2.0?, 0]:(a) what is the position of the object at time? = 2.1 ? assuming the object started at theorigin?(b) what is the distance the object has traveled at? = 2.1 ??(c) what is the velocity of the object as a functionof time?(d) what is the velocity of the object at ? = 0, ? =2.1 ? and ? = 4.2 ??(e) what is the speed of the object at the timesgiven in part (d). Are the speed evenly spaced?Would you expect this? Why or why not?(f) what is the acceleration of the object at? = 0, ? = 2.1 ? and ? = 4.2 ??A rhinoceros is at the origin of coordinates at time t1 = 0. For the time interval from t1 = 0 to t2 = 12.0 s, the rhino’s average velocity has x-component -3.8 m/s and y-component 4.9 m/s. At time t2 = 12.0 s, (a) what are the x- and y-coordinates of the rhino? (b) How far is the rhino from the origin?
- At t=0, a ball is thrown with an initial velocity of magnitude 15ms-1 at 75° to the horizontal (upwards). a) Calculate the magnitudes of the vertical and horizontal components of its initial velocity. b) Calculate the magnitude of the vertical component of velocity of the ball at t=0.5s. c) Calculate the magnitude of the vertical component of velocity of the ball at t=2.0s. d) Which way is the ball moving at this time? e)What is the magnitude of the horizontal component of velocity at t=2.0s?A football quarterback is moving straight backward at a speed of 2.00 m/s when he throws a pass to a player 18.0 m straight downfield. (a) If the ball is thrown at an angle of 25° relative to the ground and is caught at the same height as it is released, what is its initial speed relative to the ground? (b) How long does it take to get to the receiver? (c) What is its maximum height above its point of release?A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of vo= 13.0 m/s. The cliff is h = 47.0 m above a flat, horizontal beach as shown in the figure. (a) What are the coordinates of the initial position of the stone? Xo = Yo= (b) What are the components of the initial velocity? Vox m/s m/s Voy Vx= (c) Write the equations for the x- and y-components of the velocity of the stone with time. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not include units in your answer.) = m m X= (d) Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.) y =
- A particle moves in a circular path according to the clockwise equation θ(t)=π/4+3t+2t2, where θ is the angle between the particle's position vector and the x axis, oriented positively counterclockwise. θ is measured in radians and t in seconds. Which of the drawings qualitatively represents the velocity vectors v (in red) and acceleration a (in blue) of the particle at time t=0? Choose an option : A, B, C, D, E, F, G, or HA particle leaves the origin with an initial velocity of ( 2.40 m/s ) x^ , and moves with constant acceleration of ( − 1.90 m/s 2 ) x ^ + ( 3.20 m/s 2 ) y ^ . (a) How far does the particle move in the x direction before turning around? (b) What is the particle’s velocity at this time? (c) Plot the particle’s position at t= 0.500 s , 1.00 s, 1.50 s, and 2.00 s. Use these results to sketch position versus time for the particle.A particle located initially at (1.5ˆj + 4.0ˆk) m undergoes a displacement of (2.5ˆi+ 3.2ˆj − 1.2ˆk) m. (a) What is the final position of the particle? (b) If the time needed to displace the particle from its initial position to its final position is 5 s, determine the particle’s average velocity vector.