A particle initially located at the origin has an acceleration of a = 1.00ĵ m/s² and an initial velocity of v = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). tî + 1²j)m (b) Find the velocity of the particle at any time t. tj) m/s (c) Find the coordinates of the particle at t = 3.00 s. X = y = (d) Find the speed of the particle at t = 3.00 s. m/s

Part A)  A projectile is launched with speed v0v0 and angle θθ. Derive an expression for the projectile's maximum height hh. Express your answer in terms of the variables v0v0, θθ, and appropriate constants.   Part B)  A baseball is hit with a speed of 34.0 m/sm/s . Calculate its height if it is hit at an angle of 30.0 ∘∘ . Express your answer with the appropriate units.   Part C)  A baseball is hit with a speed of 34.0 m/sm/s . Calculate its distance traveled if it is hit at an angle of 30.0 ∘∘ . Express your answer with the appropriate units.   Part D  A baseball is hit with a speed of 34.0 m/sm/s . Calculate its height if it is hit at an angle of 45.0 ∘∘ . Express your answer with the appropriate units.   Part E)  A baseball is hit with a speed of 34.0 m/sm/s . Calculate its distance traveled if it is hit at an angle of 45.0 ∘∘ . Express your answer with the appropriate units.

A remote-controlled car is moving around in a level (horizontal) parking lot. The velocity of the car as a function of time is given by: 3 = [5.0m/s – (0.018m/s³)t²]î + [2.0m/s + (0.55m/s²)t]j where î and ĵ are unit vectors representing two perpendicular directions on the horizontal ground (think of them as the East and North directions, if that helps you). b). What are the magnitude and direction of the car's velocity at t = 8.0 s? c). What are the magnitude and direction of the car's acceleration at t = 8.0 s? (Don't be intimated by the velocity function! Look at the î and ĵ components, and work each component separately to begin with, before combining components together to get any resultant vectors, if needed.)

Obtain expressions in component form for the position vectors having the following polar coordinates. (a) 12.2 m, 140° counterclockwise from the +x axis R = m (b) 3.80 cm, 80.0° counterclockwise from the +x axis R cm (c) 20.0 in., 222° counterclockwise from the +x axis in.