The drag-free motion of a particle is defined by the following component equations in the X, Y Cartesian coordinate system: 1. 2 h = (Vo cos α) t and Ty = (Vo sin α) t -, 1 2 where Vo-200 m/s, α-60° and g-9.81 m/s. At t-40 s, find the components of the velocity and acceleration vectors in the X, Y Cartesian coordinates. Draw vector diagrams of the velocity and acceleration vectors in the Cartesian coordinates, including the unit vectors. 2. The velocity components of a particle are given as The initial conditions of position are r t0)y(t). Att 1s: (a) Find the components of the position and acceleration vectors in the Cartesian coordinates. (b) Determine the velocity and acceleration components in the Polar coordinates (c) Draw vector diagrams to demonstrate that the same velocity and acceleration vectors are obtained for both the Cartesian and Polar coordinate systems. Use the vector diagrams to show the vector components, unit vectors, and units.

4. A stunt plane flying at the Reno Air Races is moving through the sky. The rectangular coordinates describing its motion are: x = -0.74t³ + 2.5t² + 10.25t y = -6.23t² + 16.45t + 8.94 where x and y are given in ft and t is given in seconds. a. Calculate the velocity vector, v, and acceleration, a, of the plane after 10 seconds (velocity is in ft/s and acceleration is in ft/s²). You may want to look back at your Topic 2 notes to recall how position, velocity, and acceleration are related. Your final answer should be given in vector form. b. Calculate the magnitude of the velocity (in mph) and the acceleration (in ft/s²) at t = 10 sec. [Ans. to Check: v = 132.46 mph; a = 41.32 ft/s²]

hello, can you do a step by step solution with explaination for me thank you so much

1 Velocities are measured at different locations using a data logger and the field is given by the technician in the following vector form. Given that. du du ax = +u-+v. +w du du ôt əx ду əz V = 3tî +xzj+t Find the magnitude of velocity and acceleration at point (1,1,1) at time t = 1 second. Write the acceleration vector. If the fluid is incompressible, show that the flow field satisfies the conservation of mass. zj+ty²k m/s Əv dv dv Əv +u- +v +w- at Əx ду əz dw dw dw dw + w a ₂ = +u Ət Əx dy əz +v