十万火急～.1) A particle initially located at the origin has an a

十万火急～.
1) A particle initially located at the origin has an acceleration of = 2.00 m/s2 and an initial velocity of 0 = 7.00 m/s.
(a) Find the vector position at any time t (where t is measured in seconds).
(____t + ____t2 ) m
Find the vector velocity at any time t.
( ___ + ____t ) m/s
(b) Find the coordinates of the particle at t = 2.00 s.
x = ___ m
y = ____ m
Find the speed of the particle at this time.
____ m/s
2)Consider a planet of radius 5.93 106 m with a rotation period of 21.8 hours.Compute the radial acceleration of a point on the surface of the planet at the equator due to its rotation about its axis.
_______ m/s2 (directed toward the center of the planet)
3) A juggler performs in a room with a ceiling 2.58 m above hand level.What is the maximum upward speed (in m/s) which she can give a ball without letting it hit the ceiling?
________ m/s
4) A ball is tossed from an upper-story window of a building.The ball is given an initial velocity of 8.60 m/s at an angle of 16.0° below the horizontal.It strikes the ground 6.00 s later.
(a) How far horizontally from the base of the building does the ball strike the ground?
______ m
(b) Find the height from which the ball was thrown._______ m
(c) How long does it take the ball to reach a point 10.0 m below the level of launching?
________ s
6) A car travels due east with a speed of 45.0 km/h.Raindrops are falling at a constant speed vertically with respect to the Earth.The traces of the rain on the side windows of the car make an angle of 45.0° with the vertical.Find the velocity of the rain with respect to the following reference frames.
(a) the car
__________ m/s
(b) the Earth
_________ m/s