A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t = 0s, the x components of the puck's initial velocity and acceleration are vox = +8.3 m/s and ax = +4.1 m/s². The y components of the puck's initial velocity and acceleration are Voy = +9.5 m/s and ay = -5.4 m/s². Find (a) the magnitude v and (b) the direction of the puck's velocity at a time of t = 0.50 s. Specify the direction relative to the +x axis. (a) v = (b) 0 = i i degrees the +x axis
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- A jet airliner moving initially at 2.60 ✕ 102 mi/h due east enters a region where the wind is blowing at 1.00 ✕ 102 mi/h in a direction 25.0° north of east. (Let the x-direction be eastward and the y-direction be northward.) (a) Find the components of the velocity of the jet airliner relative to the air, vJA. vJA,x = ? mi/h vJA,y = ? mi/h (b) Find the components of the velocity of the air relative to Earth, vAE. vAE,x = ?mi/h vAE,y = ?mi/h (c) What are the speed and direction of the aircraft relative to the ground? magnitude mi/h direction ° north of eastA puck is moving on an air hockey table. Relative to an x, y coordinate system at time t = 0 s, the x components of the puck's initial velocity and acceleration are v0x = +5.6 m/s and ax = +9.5 m/s2. The y components of the puck's initial velocity and acceleration are v0y = +3.1 m/s and ay = -3.0 m/s2. Find (a) the magnitude v and (b) the direction θ of the puck's velocity at a time of t = 0.50 s. Specify the direction relative to the +x axis.The velocity v→ of a particle moving in the xy plane is given by v→=(5.50t-5.00t2)î+9.00ĵ, with v→ in meters per second and t (> 0) in seconds. At t = 1.40 s and in unit-vector notation, At what positive time does the speed equal 10.0 m/s?
- A football is placed at rest on the field with initial coordinates x0 = 0 and y0 = 0. The ball is then kicked and thereby given an initial velocity of magnitude v0 = 23.6 m/s and direction θ0 = 36.3o above the horizontal. Ignore the effects of air resistance. Initial horizontal component of the velocity v0x = Initial vertical component of the velocity v0y = Horizontal component of the acceleration ax = Vertical component of the acceleration ay = Enter the equation for the horizontal position versus time, x(t) = Enter the equation for the vertical position versus time, y(t) = Enter the equation for the horizontal velocity versus time, vx(t) = Enter the equation for the vertical velocity versus time, vy(t) = Enter the equation for the total velocity versus time, v(t) = Enter the equation for the angle of the velocity vector versus time, θ(t)= Enter the maximum height of the football Enter the range of the football Enter the time it takes for the football to reach its maximum…A student at the top of a building of height h throws one ball upward with a speed of vi and then throws a second ball downward with the same initial speed vi. Just before it reaches the ground, is the final speed of the ball thrown upward (a) larger, (b) smaller, or (c) the same in magnitude, compared with the final speed of the ball thrown downward?The velocity of a particle moving in the x-y plane is given by (6.98i + 6.68j) m/s at time t = 7.60 s. Its average acceleration during the next 0.014 s is (4.1i + 5.4j) m/s2. Determine the velocity v of the particle at t = 7.614 s and the angle θ between the average-acceleration vector and the velocity vector at t = 7.614 s.Answers:v = ( _____ i + _____ j) m/sθ = _____ °
- A glider is initially moving at a constant height of 3.76 m. It is suddenly subject to a wind such that its velocity at a later time t can be described by the equation v(t) = 16.18 − 7.78(1 + t) + 0.70t3, where v and its components are in meters per second, t is in seconds, and the z axis is perpendicular to the level ground. (a) What was the initial velocity of the glider? (Express your answer in vector form.) vi = m/s(b) Write an expression for the acceleration of the glider in component form when t = 2.14 s. (Express your answer in vector form.) a(t = 2.14 s) = m/s2A jet airliner moving initially at 3.35 ✕ 102 mi/h due east enters a region where the wind is blowing at 1.00 ✕ 102 mi/h in a direction 29.5° north of east. (Let the x-direction be eastward and the y-direction be northward.) (a) Find the components of the velocity of the jet airliner relative to the air, vJA. vJA,x = mi/h vJA,y = mi/h (b) Find the components of the velocity of the air relative to Earth, vAE. vAE,x = mi/h vAE,y = mi/h (d) What are the speed and direction of the aircraft relative to the ground? magnitude mi/h direction ° north of eastOn a spacecraft two engines fire for a time of 532 s. One gives the craft an acceleration in the x direction of ax = 4.92 m/s2, while the other produces an acceleration in the y direction of ay = 7.16 m/s2. At the end of the firing period, the craft has velocity components of vx = 3743 m/s and vy = 4808 m/s. Calculate the magnitude of the initial velocity.
- Consider the motion of a bullet that is fired from a rifle 3 m above the ground in a northeast direction. The initial velocity of the bullet is150,150,0. Assume the x-axis points east, the y-axis points north, the positive z-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts on the object. a. Find the velocity and position vectors for t≥0. b. Make a sketch of the trajectory. c. Determine the time of flight and range of the bullet. d. Determine the maximum height of the bullet.At t=0, a ball is thrown with an initial velocity of magnitude 15ms-1 at 75° to the horizontal (upwards). The magnitudes of the vertical and horizontal components of its initial velocity are 14.49 m/s and 3.88 m/s. The magnitude of the vertical component of velocity of the ball at t=0.5s is 9.585 m/s. The magnitude of the vertical component of velocity of the ball at t=2.0s is 5.13 m/s. Which way is the ball moving at this time? What is the magnitude of the horizontal component of velocity at t=2.0s?A jet airliner moving initially at 3.35 102 mi/h due east enters a region where the wind is blowing at 1.00 102 mi/h in a direction 35.5° north of east. (Let the x-direction be eastward and the y-direction be northward.) (a) Find the components of the velocity of the jet airliner relative to the air, JA. vJA,x = mi/h vJA,y = mi/h (b) Find the components of the velocity of the air relative to Earth, AE. vAE,x = mi/h vAE,y = mi/h (c) Write an equation analogous to vAB = vAE − vBE for the velocities vJA, vAE, and vJE . (In the given equation, vBE is the velocity of observer B relative to observer E. Object A travels with velocity vAB relative to observer B, and velocity vAE relative to observer E.) vJA = vJA = vAE + 2vJE vJA = vAE − vJE vJA = vJE − vAE vJA = vJE + vAE (d) What are the speed and direction of the aircraft relative to the ground? magnitude mi/h direction ° north of east