Conservation of momentum and jumping girl

[nns91]

Homework Statement

1. A force F= 12 N i is applied to a 3kg ball which has coordinate of (2,2). What is the acceleration of the center of mass.

2. A girl jumps from a boat to a dock. Why does she have to jump with more energy than she would need if she were jumping the same distance from one dock to another ?

3. A shell of mass m and speed v explodes into two identical fragments. If the shell ws moving horizontally with respect to the earth, and one of the fragments is subsequently moving vertically with the speed v, find the velocity v' of the other fragment.

4/ In a circus act, Marcello (m= 70kg) is shot from a cannon with a muzzle velocity of 24 m/s at an angle of 30 degree above horizontal. His partner, Tina (m=50kg), stands on an elevated platform located at the top of his trajectory. He grabs her as he flies by and the two fly off together. They land in a net at the same elevation as the cannon a horizontal distance x away. Find x

5. Liz, Jay, and Tara discover tha sinister chemicals are leaking at a steady rate from a hole in the bottom of a realiway car. To collect evidence of a potential environmental mishap, they videotape the car as it rolls without friction at initial speed of v₀. Tara claims that the car's speed is increasing, because it is losing mas as it drains. The increase in speed will help to prove that the leak is occurring. Liz says no, that with a loss of mass, the car's speed will be decreasing. Jay says the speed will remain the same. (a) who is right ? (b) what forces are exerted on the system of the car plus chemical cargo ??

Homework Equations

F=ma
Mv_cm=m1v1 + m2v2

The Attempt at a Solution

1. I use F= M a(i) so a = F/m = 12N/3kg = 4 m/s^2. However, I got marked wrong. Where did I do wrong ??

2. I explained that because when she jumps from the boat, the boat will have a velocity of opposite direction. However, when she jumps from dock to dock, the dock does not move. Thus, she needs more energy to jump from the boat.

p1=m1v1 + m2v2 > p2=m1v1 m1v1 are of the girl and m2v2 are of the boat.

Why my explanation is wrong ??

3. Mv_cm= (m/2)v1 + (m/2)v2

In x component: Mv_cm,x = (m/2)*0 + (m/2)*v2

Thus, v= (1/2)v2 so v2= 2v. What did I do wrong again ?

4. I use R=(v^2* sin2$$\theta$$)/g to find x and get (24^2* sin60)/9.81 = 50.8m

How can I fix this mistake ??

5. I answered that Tara was right because as Mv_cm= m1v1 +m2v2 so

v_cm= (m1v1+m2v2) / (m1+m2) and m2 (mass of oil) decreases v will increases. However, I am wrong again.

I think Liz was right since you don't have that much of fuel and car's speed will approach zero. I don't know how to explain in a right way. AM I right ?

(b) I got normal force and gravitational force. Are those enough ??

 

[radou]

First of all, what is the direction of the applied force in 1. ?

 

[nns91]

1. It's in x direction.

 

[nns91]

In number one, the i means x direction in unit vector notation.

 

[nns91]

I have trying to solve number 4 but still got wrong answer. Anyone have any ideas ?