<span>The ball with an initial velocity of 2 m/s rebounds at 3.6 m/s
The ball with an initial velocity of 3.6 m/s rebounds at 2 m/s
There are two principles involved here
Conservation of momentum and conservation of energy.
I'll use the following variables
a0, a1 = velocity of ball a (before and after collision)
b0, b1 = velocity of ball b (before and after collision)
m = mass of each ball.
For conservation of momentum, we can create this equation:
m*a0 + m*b0 = m*a1 + m*b1
divide both sides by m and we get:
a0 + b0 = a1 + b1
For conservation of energy, we can create this equation:
0.5m(a0)^2 + 0.5m(b0)^2 = 0.5m(a1)^2 + 0.5m(b1)^2
Once again, divide both sides by 0.5m to simplify
a0^2 + b0^2 = a1^2 + b1^2
Now let's get rid of a0 and b0 by assigned their initial values. a0 will be 2, and b0 will be -3.6 since it's moving in the opposite direction.
a0 + b0 = a1 + b1
2 - 3.6 = a1 + b1
-1.6 = a1 + b1
a1 + b1 = -1.6
a0^2 + b0^2 = a1^2 + b1^2
2^2 + -3.6^2 = a1^2 + b1^2
4 + 12.96 = a1^2 + b1^2
16.96 = a1^2 + b1^2
a1^2 + b1^2 = 16.96
The equation a1^2 + b1^2 = 16.96 describes a circle centered at the origin with a radius of sqrt(16.96). The equation a1 + b1 = -1.6 describes a line with slope -1 that intersects the circle at two points. Those points being (a1,b1) = (-3.6, 2) or (2, -3.6). This is not a surprise given the conservation of energy and momentum. We can't use the solution of (2, -3.6) since those were the initial values and that would imply the 2 billiard balls passing through each other which is physically impossible. So the correct solution is (-3.6, 2) which indicates that the ball going 2 m/s initially rebounds in the opposite direction at 3.6 m/s and the ball originally going 3.6 m/s rebounds in the opposite direction at 2 m/s.</span>
Answer:
.c. −160°C
Explanation:
In the whole process one kg of water at 0°C loses heat to form one kg of ice and heat lost by them is taken up by ice at −160°C . Now see whether heat lost is equal to heat gained or not.
heat lost by 1 kg of water at 0°C
= mass x latent heat
= 1 x 80000 cals
= 80000 cals
heat gained by ice at −160°C to form ice at 0°C
= mass x specific heat of ice x rise in temperature
= 1 x .5 x 1000 x 160
= 80000 cals
so , heat lost = heat gained.
In order to find the force (F), you would have to use the formula for it:
F=ma
where m is mass and a is acceleration.
In the problem, the mass is 2.85kg and the acceleration is 4.9m/s^2.
Therefore,
F=2.85kg(4.9m/s^2)
F=13.965kg(m/s^2)
Since N=kg(m/s^2)
F=13.965N
And because the problem requires that we use only 2 significant figures,
F=13N
Therefore, the student must exert 13N of force.
Coastal erosion has depleted a large portion of South Louisiana's wetlands along the coastline in swamps and marshes mainly due to storm surges. But other factors also contributed to this erosion. Canals and waterways dug through the marshes and swamps for the oil industry is one factor. Man-made levees erected to provide protection to residents living adjacent to the river is another major cause. Large scale logging especially in the early 1900's also damaged the wetlands.
