A у -plane a velocity given by 2.4 m/s, B = 1.6 m/s³ and y = 4.0 m/s². The positive y -direction is At t = 0 the bird is at the origin. %3D ulate the position and acceleration vectors of the bird as functions of tim 14itude (o it Aiog O fon t he fngt +
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- The velocity of a particle is V and is constant. It moves counterclockwise on a circle with center "O" and radius R. Draw the circle. When the particle is in the vector R position, draw vector R, vector V, vector A, and vector da/dt(time derivative of acceleration).A physics student adds two displacement vectors with magnitudes of 8.0 km and 6.0 km. Which one of the following statements is true concerning the magnitude of the resultant displacement? O It must be 14.0 km. No conclusion can be reached without knowing the directions of the vectors. It must be 10.0 km. O It could have any value between 2.0 km and 14.0 km depending on how the vectors are oriented. O It could be equal to zero kilometers, depending how the vectors are oriented.A rectangular parallelepiped has dimensions a, b, and c as shown in Figure P3.45. (a) Obtain a vector expression for the face diagonal vector R,. (b) What is the magnitude of this vector? (c) Notice that R, ck, and R, make a right triangle. Obtain a vector expression for the body diagonal vector R2. b Ro R1 Figure P3.45
- Let W = (x²y, y³z, xyz). Determine V.Ŵ.Q/ A particle moves in an xy plane according to x(1)= -20.00 + 20.00t - 4.00 and y(t) = 25.00 + 17.00t -19.00², with x and y in meters and t in seconds. At t= 10 s, a. What is the particle velocity vector vì nunit vector notation? b. What is the particle acceleration vector đìn unit vector notation?A particle starts from rest at the origin with an acceleration vector that has magnitude 6.0 m/s2m/s2 and direction 35 ∘∘ above the positive x axis. A) A particle starts from rest at the origin with an acceleration vector that has magnitude 6.0 m/s2 and direction 35degrees above the positive x axis. B)What is the vy component of its velocity vector 23 s later? C)What is the particle’s dx position at that time? D)What is the particle’s dy position at that time?
- A projectile is fired upward at an angle of 36.1 above the horizontal with an initial speed v; = 5.0 m/s. Write down the velocity vector v (in m/s) and the acceleration vector a (in m/s?) of the projectile at its maximum height in unit vector notations i and j O there is no answer O v= 2i + 0j m/s, a= 0i – 10j m/s? O v= 4i + 0j m/s, a = 0i – 10j m/s² O v= 5i + 0j m/s, a = 0i + 10j m/s? O v= 3i + 0j m/s, a = 0i + 10j m/s?Trachecktory. Two cannonballs, aptly named a and ß, were launched on level ground. a was launched with a velocity of 18.0 [m/s] at 36° with respect to the ground while ß was launched with a velocity of 17.6 [m/s] at 48° with respect to the ground. What can you say about a and ß's range and time of flight? O a and ß do not have the same range; a has a larger time of flight. O a and ß have the same range; a has a larger time of flight. a and ß have the same range; ß has a larger time of flight. a and ß do not have the same range; ß has a larger time of flight.The x- and y-coordinates of a projectile launched from the origin are x = Vort and y = voyt – ¿gt². Solve the first of these equations for time t and substitute into the second to show that the path of a projectile is a parabola with the form y = ax + bx, where a and bare constants.
- You stand at the edge of a 22.0 m high cliff and throw a stone straight down with a speed of 8.00 m/s. Before it hits the ground, the stone is traveling with a speed of 22.3 m/s. Let down be the positive vertical direction. Using the given coordinate system, what is the sign of the displacement of the stone from the point it is released until just before it hits the ground? O Negative Zero O PositiveA runner runs along the helix r(t) = (cost,sin t,t). When he isat position r( π/2), his speed is 3 m/s and he is accelerating at a rate of1/2 m/s2. Find his acceleration vector a at this moment. Note: The runner’s acceleration vector does not coincide with the acceleration vectorof r(t).When t = 0 the particle is at A. In four seconds it travels to B, then in another six seconds it travels to C. Determine the average velocity and the average speed. The origin of the coordinate is at O.