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Q: Tarzan, who weighs 688N, swings from a cliff at the end of a vine that is 18m long. From the top of the cliff to the bottom of the swing, he descends by 3.2m. The vine will break if the force on it exceeds 950N. a)Does the vine break? b) If no, what is the greatest force on it during the swing? If yes, at what angle with the vertical does it break?

A:From energy conversation principle' from the point A to the point B
mgh = 1/2 mv2
0r v2 = 2gh

The mass of the person m = W / g
= 688 / 9.9 = 70.2kg

From the figure we see,
T - mg = mv2 / R
T = mg + mv2 / R
substituting for v 2 we get
T = mg ( 1 + 2h/R )
or T = 933N
As the force does not exceed 950N the vine will not break.

b) The maximun tension T = 9.326*102N

I think?

also...

Q: A 0.88 kg ball drops vertically onto a floor, hitting with a speed of 33 m/s. It rebounds with an initial speed of 13 m/s. (a) What impulse acts on the ball during the contact? (b) If the ball is in contact with the floor for 0.0397 s, what is the magnitude of the average force on the floor from the ball?

A: I = mvf - mvi
I = m(vf - vi)
I = 0.88(.13-33)
I = -40.48 J

if the contact time = 0.0397 s, then:
F = Äp/Ät = I/Ät = -40.48/0.0397
F = -1019.65 J, or -1.9x103 N




1 You worked correctly, I did not check the math.
2. You missed a negative sign, the ball rebound velocity is opposite to the direction initial. So you minus a negative, or add the velocities.

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