1.)  Let s(t)= tlnt-t be the displacement of a particle (in feet) from the origin after t seconds.   a.) Find the velocity of the particle at 5 seconds. (Show all your work and include units)   b.) Find the acceleration of the particle after 5 seconds. (Show all your work and include units)

A ball is launched from ground level at 30 m/s at an angle of 35˚ above the horizontal.   (a) Find the speed of the ball when it reaches the maximum height.   (b) How far does it travel horizontally just  before impacting with the ground? A.) (a)   0,    (b)  98 m B.) (a)  0,          (b)  86.3 m C.) (a)  24.6 m/s,    (b) 86.3 m D.) (a)  17.5 m/s,     (b) 90.8 m

A basket of flowers of mass 3 kg is placed on a flat grassy slope that makes an angle θ with the horizontal. The coefficient of static friction between the basket and the slope is 0.45 and the basket is on the point of slipping down the slope. Model the basket of flowers as a particle and the grassy slope as a plane. Take the magnitude of the acceleration due to gravity, g, to be 9.8 m s−2 Express the forces in component form, in terms of θ and unknown magnitudes where appropriate. Write down the equilibrium condition for the basket and hence show that tan θ = 0.45. Determine the angle, in degrees, that the slope makes with the horizontal.

A sheet of water of uniform thickness (h = 0.03 m) flows from the device shown in the figure below. The water enters vertically through the inlet pipe and exits horizontally with a speed that varies linearly from 0 to 11 m/s along the 0.2-m length of the slit. Determine the y component of anchoring force necessary to hold this device stationary. FAY = 0 m/s- i 0.2m 0.03m N 11m/s