A child in a boat throws a 6.00 kg package out horizontally with a speed of 13.0 m/s, Fig. 7-28. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 28.0 kg and that of the boat is 50.0 kg.
I could find the velocity if I had the time interval, but I dont. But there is no time interval....how can I find it?
2006-12-11 18:13:09 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Physics
(Ma)(Va)+(Mb)(Vb)=(Ma)(Va')+(Mb)(Vb')
initial (Va) and (Vb) are zero so
(Ma)0+(Mb)0=(Ma)(Va')+(Mb)(Vb')
0=(Ma)(Va')+(Mb)(Vb')
-(Ma)(Va')=(Mb)(Vb')
-(Ma)(Va')/(Mb)=(Vb')
(Vb') will be negative meaning that it is moving in a direction oposite to that of the package. if you set (Va') negative (Vb') will be positive
2006-12-11 20:47:28 · answer #1 · answered by cfoos1 1 · 1⤊ 0⤋
guess. The time interval (distance / speed = time) can be roughly extrapolated by estimating, which is then confirmed and/or adjusted to accuracy via calculation.
Estimating is the second action all mathematicians must undergo, after understanding the problem (first). This has 2 purposes:
1) by making an initial estimation before attempting to solve the problem in long hand, one has a ball park figure which one knows is posibly incorrect, so a field of error is assumed call the ball park in which the ball may land. if it does not, then it is possible the long hand is incorrect, so double check it. Otherwise, the estimation is incorrect, and one must then determine one's mistake to learn how to be a better estimator. This in turn makes the next problem easier by having a ball park in which to work. QED.
2) Also, by being a good estimator one can often skip stages of the calculation process in circumstances where an accurate measurement is unncessesary, and this has excellent real world application. Example: Your in the supermarket looking at which chocolate bar to buy, and want to know which one is best value for money. Each bar has a different mass, volume, taste and price, but the differences are small between them. You could get out a calculator, and bring each bar's mass to a single base line to compare the price per gram, or per cubic metre, and look like a geek in the process, or use the skills developed by estimating problems appointed by your physics teacher to make a calculated guess in a few seconds and maybe even save your friends some money to boot by sharing your unsubstantiated "feeling".
Guess again!
2006-12-12 03:47:06 · answer #2 · answered by Bawn Nyntyn Aytetu 5 · 1⤊ 0⤋
for reasons that you wouldnt be interested in, momentum (the product of velocity and mass) is conserved. what this means is that for any physical transaction the vector sum of momentum for ideal (infinetely hard in the macroscopic world where particle momentum doesnt need to be taken into account) objects is zero. in order to maintain this law in this case when the package is thrown with a momentum of (6 kg)(13 m/s)= 78 kg*m/s in the horizontal direction, the boat and the kid in it must react by equallizing its own momentum to cancel out the new momentum created by throwing the package. because its mass is 50 + 28 = 78 kg the velocity must be (78 kg*m/s)/78 kg = 1 m/s in the direction opposite to that of the package.
2006-12-12 05:56:50 · answer #3 · answered by will i know people in heaven? 2 · 1⤊ 0⤋
You don't need the time: it is an ENERGY problem.
The energy of the package is M x Speed.
The boad (and the kid) receive the same energy, in opposite direction.
Since the boat is 28K + 50Kg, you get the speed...
(remember Newton's laws: a force has an equal and opposite reaction force. Same with energy when you tranfer it...)
2006-12-12 04:29:21 · answer #4 · answered by just "JR" 7 · 1⤊ 0⤋