View Policies Current Attempt in Progress At time t = 0, the position vector of a particle moving in the x-y plane is r = 5.30i m. By time t = 0.016 s, its position vector has become (5.56i + 0.47j) m. Determine the magnitude Vay of its average velocity during this interval and the angle made by the average velocity with the positive x-axis. Answers: = Vav m/s O i i
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- The vector position of a particle varies in time according to the expression r (3.00i 6.00t 2 j) m. (a) Findexpressions for the velocity and acceleration as functions of time. (b) Determine the particle’s position andvelocity at t 1.00 sA particle initially located at the origin has an acceleration of = 1.00ĵ m/s2 and an initial velocity of i = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). (b) Find the velocity of the particle at any time t. (c) Find the coordinates of the particle at t = 3.00 s. (d) Find the speed of the particle at t = 3.00 s.A particle initially located at the origin has an acceleration of a⃗ = 3.0ĵm/s2 and an initial velocity of vi = 500îm/s Find (a) the vector position and velocity at any time t and (b) the coordinates and speed of the particle at t = 2.00 s.
- A particle initially located at the origin has an acceleration of = 2.00ĵ m/s2 and an initial velocity of i = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds).( t î + t2 ĵ) m(b) Find the velocity of the particle at any time t.( î + t ĵ) m/s(c) Find the coordinates of the particle at t = 3.00 s.x = my = m(d) Find the speed of the particle at t = 3.00 s. m/sA particle starts from the origin at t=0, with an initial velocity having an x component of 20m/s and a y component of -15m/s. The particle moves in the xy plane with an x component of acceleration only, given by Ax =4.0 m/s^2 Determine the components of the velocity vector at anytime and the total velocity vector at any time . Calculate the velocity and speed of the particle at t=5.0s.A particle initially located at the origin has an acceleration of = 4.00ĵ m/s2 and an initial velocity of i = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds).( t î + t2 ĵ) m(b) Find the velocity of the particle at any time t.( î + t ĵ) m/s(c) Find the coordinates of the particle at t = 7.00 s.x = my = m(d) Find the speed of the particle at t = 7.00 s.m/s
- A cannon ball is fired with an initial speed of 123 m/s at angle of 60 degrees from the horizontal. Express the initial velocity as a linear combination of its unit vector components. ( m/s) + ( m/s) At the maximum height, the speed of the cannon ball is v = ? m/s and the magnitude of its acceleration is a = ? m/s2. The time needed to reach maximum height is t = ? s. The maximum height reached by the cannon ball is H = ? m.You can use any coordinate system you like in order to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v at an angle ? with respect to the horizontal. Let the building be 54.0 m tall, the initial horizontal velocity be 8.60 m/s, and the initial vertical velocity be 12.5 m/s. Choose your coordinates such that the positive y-axis is upward, and the x-axis is to the right, and the origin is at the point where the ball is released. (a) With these choices, find the ball's maximum height above the ground and the time it takes to reach the maximum height. maximum height above ground m time to reach maximum height s (b) Repeat your calculations choosing the origin at the base of the building. maximum height above ground m time to reach maximum height sFor projectile motion problems, the horizontal and vertical components of the motion of a projectile can be analyzed separately. Which of the following is TRUE about the horizontal component of its motion?a. The horizontal component of the acceleration is constant and is equal to -9.81 m/s^2b. The motion is uniformc. The horizontal component of the velocity varies with positiond. The motion is uniformly accelerated
- A particle moves along xy-plane with a position of x (t) = sin(2t) + 3 cos(4t) y (t) = 1/2 sin(t) – 6 cos(3t) a. Determine the position vector of the particle. b. Determine the velocity vector of the particle. c. Determine the acceleration vector of the particle. d. Determine the position vector of the particle when t = 4s. e. Determine the average acceleration from t = 0s to t= 5s. f. Determine the instantaneous acceleration when t= 1s. g. Determine the average velocity from t = 1s to t= 3s.You can use any coordinate system you like to solve aprojectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building witha velocity vS at an angle u with respect to the horizontal. Letthe building be 50.0 m tall, the initial horizontal velocity be9.00 m/s, and the initial vertical velocity be 12.0 m/s. Chooseyour coordinates such that the positive y - axis is upward, thex - axis is to the right, and the origin is at the point where theball is released. (a) With these choices, find the ball’s maximumheight above the ground and the time it takes to reachthe maximum height. (b) Repeat your calculations choosingthe origin at the base of the building.In the two-dimensional motion, what is the magnitude of the y component of the velocity of the projectile when it is at its apex of trajectory? Select one: a. Velocity is equal to the initial velocity b. Velocity is 9.81 m/s c. Velocity is equal to the x component d. Undetermined e. Velocity is 0 m/s