DYNAMICS

A balloon rises from the ground with a constant acceleration of 4ft per sec^2. Five seconds later, a stone is thrown vertically up from the launching site. What must be the minimum initial velocity of the stone for it to just touch the balloon? Note that the balloon and stone have the same velocity at contact.

Moment Area theorem problem. please help

I've been trying to solve the following question for 2 days now and i can't seem to be able to. can someone help me please ?

For the beam shown in Figure 3, the support at A is fully fixed. The beam is tapered however you may consider it to be a beam of 3 varying sections.

Take:
Beam A to B as having 3 times the I value of beam D to end, Beam B to D as having 1.5 times the I value of beam D to end and Beam D to end is 310 UB 46.2 with I = 100 x 106 mm4. Tip: this may be easier to solve using superposition.

Need help po

A constant horizontal force of 10 lb rests on a body of smooth horizontal plane. The body starts from rest and is observed to move 250 ft in 5s.
a). What is the mass of the body?
b). If the force ceases to act at the end of 5s, how far will the body move in the next 5s?

Help please :( - Flange Bolt coupling

A flanged bolt coupling consists of two concentric bolt circles. One bolt circle consists of six 0.5-in-diameter steel bolts on a circle 9 inches in diameter and the other consists of eight 0.5-in-diameter steel bolts on a circle 12 inches in diameter. What is the shearing stress in the bolts if a torque of 7 kip-ft is to be carried by the assembly?