I am really struggling with these two questions. Please help!
1)Two ice skaters approach each other at right
angles. Skater A has a mass of 61.2 kg and
travels in the +x direction at 2.25 m/s. Skater
B has a mass of 66.2 kg and is moving in the
+y direction at 1.3 m/s. They collide and
cling together.
Find the final speed of the couple.
Answer in units of m/s.
2)A 1.46 kg skateboard is coasting along the
pavement at a speed of 5.24 m/s when a 0.710
kg cat drops from a tree vertically downward
onto the skateboard.
What is the speed of the skateboard-cat
combination? Answer in units of m/s.
Thank you!
second problem same Newton One stuff.
1) Ah, the classic ice skating collision. It's like a dance, but with less grace and more sliding. Now let's see what's happening here. Skater A is moving in the +x direction, while Skater B is moving in the +y direction. They collide and cling together, forming a couple. How sweet!
To find the final speed of the couple, we need to use the principle of conservation of momentum. Momentum is conserved in collisions, which means the total momentum before the collision is the same as the total momentum after the collision. Mathematically, it can be written as:
(mass of A * velocity of A) + (mass of B * velocity of B) = (total mass of the couple * final velocity of the couple)
Plugging in the values given, we have:
(61.2 kg * 2.25 m/s) + (66.2 kg * 1.3 m/s) = (total mass of the couple * final velocity of the couple)
Now, we just need to solve for the final velocity of the couple.
2) Ah, a cat with impeccable timing, dropping onto a skateboard. Well, let's see how fast this feline-skateboard combination will be speeding away.
Again, we'll be using the conservation of momentum principle. The total momentum before the cat drops is the same as the total momentum after the cat drops. We can write it as:
(mass of the skateboard * velocity of the skateboard) + (mass of the cat * velocity of the cat) = (total mass of the combination * final velocity of the combination)
Plug in the values given:
(1.46 kg * 5.24 m/s) + (0.710 kg * 0 m/s) = (total mass of the combination * final velocity of the combination)
Since the cat was initially at rest, its velocity is 0 m/s.
Now, let's solve for the final velocity of the combination.
Remember, if you're still struggling, don't worry. Just remember that physics can be as confusing as a clown juggling chainsaws, but with a bit of humor, we can make it more bearable!
Sure, I'd be happy to help you with these questions!
1) To find the final speed of the couple after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision, assuming no external forces are involved.
We can calculate the initial momentum of skater A by multiplying the mass (61.2 kg) by the velocity (+2.25 m/s). Similarly, the initial momentum of skater B can be obtained by multiplying the mass (66.2 kg) by the velocity (+1.3 m/s).
Now, since the skaters cling together after the collision, their final momentum would be the sum of their initial momenta.
So, final momentum = initial momentum of A + initial momentum of B
Now, to calculate the final speed of the couple, we divide this total momentum by the combined mass of skater A and skater B.
Final speed = (initial momentum of A + initial momentum of B) / (mass of A + mass of B)
Plugging in the values, the final speed of the couple can be found.
2) In this question, the momentum of both the skateboard and the cat should be conserved before and after the cat drops onto the skateboard. This is because there are no external forces acting on the system.
The initial momentum of the skateboard is given by its mass (1.46 kg) multiplied by its velocity (5.24 m/s). The initial momentum of the cat is given by its mass (0.710 kg) multiplied by its initial velocity (0 m/s as it is initially at rest).
Once the cat drops onto the skateboard, they move together as a combined system. The sum of their initial momenta will be equal to the sum of their final momentum.
To find the final speed of the skateboard-cat combination, we divide the total final momentum by the combined mass of the skateboard and the cat.
Final speed = (initial momentum of the skateboard + initial momentum of the cat) / (mass of the skateboard + mass of the cat)
Again, plugging in the values into the equation will give you the final speed of the skateboard-cat combination.
I hope this helps! Let me know if you have any further questions.
x momentum = 61.2 * 2.25 FOREVER
y momentum = 66.2 * 1.30 FOREVER
so
final mass = 61.2+66.2 = 127.4
final x momentum :
127.4 * Vx = 61.2*2.25 Remember?
final y momentum
127.4 * Vy = 66.2* 1.30
final speed = sqrt(Vx^2+Vy^2)
tan theta = Vy/Vx
where theta is angle above +x axis