Recreational Problems (Physics)

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Here is one about resistance.
http://itute.com/board/viewtopic.php?t=321

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Here are another two three (aren't resistors fun):

5. A speeding motorbike passes an unmarked police car on the highway. The bike is traveling at a speed of , and the police car at a speed of . After a delay of 1 second, the police car accelerates constantly at until he catches the bike. The bike does not accelerate, but travels on at the same speed.
Calculate the distance it takes the police car to overtake the bike in terms of a, V and v.

6. In the (first) diagram, all resistors have resistance and all the ideal batteries have emf . What is the amount of current and direction of current through resistor R?

7. In the (second) diagram, , , , , , . Find the current through the battery.

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7. 6/7 A

5. From the moment the bike passed the police. (v/a){v-V+a+sqrt[(v-V)(v-V+2a)]}

6.

I=8/4=2A down

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6 and 7 are correct, but for 5 I got

Here is one about resistance.
http://itute.com/board/viewtopic.php?t=321

If the current just before P is , then the current will split equally at the junction and of current will go through each resistor. Similarly, a currrent of will go through each resistor. of current goes through the resistors because it must split again.

So the equivalent resistance is:

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For Q5
Try v=4, V=2 and a=1 to find whether the two displacements are the same.

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For Q5
Try v=4, V=2 and a=1 to find whether the two displacements are the same.

Sorry, yeah that's correct

I missed the in

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You are in a car holding a helium balloon. The car suddenly swerves to the right. In which direction will the balloon move?

[evaporade]

to the right

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correct!

[TrueTears]

A baseball with mass 0.14 kilogram and speed 40 m/s is caught.  If all of its kinetic energy is converted to heat as it is caught, and all of the heat is absorbed by the ball, what is its temperature change? (Assume the baseball's specific heat capacity is 1,000 joules per kilogram degree Celsius.)

[Mao]

+0.8 K (assuming no other forms of energy, no energy loss)

[TrueTears]

Correct.

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Another few (I haven't tried solving these yet so I hope they work but it's still ROCKET SCIENCE fo shizle)

a) The Snobbits of planet Kazak wonder what is beyond the sky, so they launch a rocket vertically upwards from the ground to take photos.
The mass of planet Kazak is and its radius is m. The material to build the rocket weighs and the rocket contains of potassium used for thrust. If the potassium is exhausted at a constant rate of and each kilogram produces of thrust, find the maximum height reached by the rocket.

b) The inhabitants of planet Australia already know the mass of their planet () but they don't know the radius. Being the practically-minded geniuses they are, they decide to send up several rockets into space and measure the speed of the rocket at infinity. Eventually they find that a rocket with the same specifications as the Snobbits' rocket is stationary at infinity. What is the radius of Australia?

[kamil9876]

a.) Why did I get some fucked up differential equation? 

Maybe there is a move clever way of doing it, it's too late 

[TrueTears]

I just have to lol at "planet Kazak"