Draw free body diagrams and show coordinate system.

Problem 1: An archer shoots an arrow vertically upward. If the arrow ascends to a maximum height of 100 feet.

a. Find the value of the initial velocity of the arrow.

b. Find the time for the arrow to attain the maximum height.

c. Find the total time that the arrow is in fight.

Problem 2: At the instant shown the velocity of collar D is 60 in/s. Upward, determine

a. The instantaneous center of Zero velocity of link BD.

b. The angular velocity of crank AB and link BD.

c. The velocity of the midpoint of link BD.

Problem 3: The block shown is observed to have a velocity v₁ = 20 ft/sec as it passes point A and a velocity v₂ = 10 ft/sec as it passes point B on the incline.

Calculate the coefficient of friction µ between the block and the incline if x = 30 ft and θ = 15 deg.

Problem 4: The 4 - kg disk shown in figure is initially at rest at time t = 0. A force of 60N is applied to the thin, inextensible cable wrapped around the disk.

a. Find the angular acceleration of the disk.

b. Find the angular velocity, and the total angular displacement of the disk 4 s after the force has been applied.

c. Find the angular velocity of the disk after this element has completed four revolutions.

Problem 5: A 30-lb slender rod AB is 5ft long and is provided above a point O which is 1 ft from end B. The other end is pressed against a spring of constant k = 1,800 lb/in. until the spring is compressed 1 in. The rod is then in a horizontal position. If the rod is released from this position, determine its angular velocity as the rod passes through a vertical position.