What Speed Does the Man Hit the Ground?

[sacsac]

Homework Statement

An 81 kg man lowers himself to the ground from a height of 10.6 m by holding onto a rope that runs over a frictionless pulley to a 60 kg sandbag.
(a) With what speed does the man hit the ground if he started from rest?

(b) What can he do to make him hit the ground slower?

Homework Equations

The Attempt at a Solution

attempt for part a: no idea... i drew diagram, labeled forces, but can't seem to go beyond that.
attempt for part b: hold the string attached to the sandbag and pull down as he is going downward.

 

[Nabeshin]

1attempt for part a: no idea... i drew diagram, labeled forces, but can't seem to go beyond that.

If you drew your free body diagram and labeled all the forces, the next step should be to write down Newton's laws. Ultimately, you want to deduce the man's acceleration.

Hint: What must be the relationship between the man's acceleration and the sandbag's acceleration?

 

[sacsac]

both accelerations should be the same shouldn't it? so this is what i have so far...

Sum of forces for m1: Ft - m1g

Sum of forces for m2: m2g - Ft

m1a = Ft - m1g

m2a = m2g - Ft

Ft = m2g - m2a

m1a = ( m2g - m2a ) - m1g

m1a + m2a = m2g - m1g

80a + 60a = 60*9.8 - 80*9.8

140a = -196

a = -1.4 m/s^2? but since the man is going down, and my reference frame for going down for a is positive, should it be 1.4? and if a = 1.4 or -1.4, how do i find the impact velocity? V^2 = Vo^2 + 2ax?...

 

[Nabeshin]

how do i find the impact velocity? V^2 = Vo^2 + 2ax?...

Your original statement of the problem says the man's mass is 81kg, yet you use 80 in your work. Typo? Either way, your work is correct. That equation will do nicely to find velocity. Remember, having acceleration (which is constant in this problem), it's just a kinematics question!

 

[sacsac]

Oh sorry about that. Yes, it forgot it was supposed to be 81. But I redid it and got the right answer! Thank You very much!