The radius of a small ball is around 3.79747 cm. The radius of a basketball is about 3.16 times larger. What is the ratio of the
1 answer:
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Answer:
For this case, if we try to find the final temperature of A and B, we see that we will obtain an expression in terms of specific heats and masses, from the information given we know the relationship between specific heats, but we don't know the relationship that exists among the masses, then the best option for this case is:
d) More information is needed
(The relation between the masses is not given)
Explanation:
For this case we know the following info:
Where c means specific heat for the substance A and B.
We also know that the initial temperatures for both sustances are equal:
We assume that we don't have melting or vaporization in the 2 substances. So we just have presence of sensible heat given by this formula:
And for this case we know that Both A and B are at the same initial temperature when equal amounts of energy are added to them, so then we have this:
And if we replace the formula for sensible heat we got:
And if we replace for the change of the temperature we got:
And since we have this:
For this case, if we try to find the final temperature of A and B, we see that we will obtain an expression in terms of specific heats and masses, from the information given we know the relationship between specific heats, but we don't know the relationship that exists among the masses, then the best option for this case is:
d) More information is needed
(The relation between the masses is not given)
Answer:
The maximum height that the fish can jump is 2.19 m.
Explanation:
Hi there!
Please, see the attached figure for a better understanding of the problem.
The motion of the salmon is a parabolic one because when it jumps, it already has a horizontal velocity (see figure).
The position and velocity vectors of the salmon at a time t, can be calculated as follows:
r = (x0 + v0x · t, y0 + v0y · t + 1/2 · g · t²)
v = (v0x, v0y + g · t)
Where:
r = position of the salmon at time t.
x0 = initial horizotal position.
v0x = initial horizontal velocity.
t = time.
y0 = initial vertical position.
v0y = initial vertical velocity.
g = acceleration of gravity.
Looking at the figure, notice that at the maximum height, the vertical velocity is zero (because the velocity vector is horizontal). Using the equation of the vertical component of the velocity, we can obtain the time at which the salmon is at its maximum height:
vy = v0y + g · t
To find the initial vertical velocity, v0y, let´s look at the figure. Notice that the initial velocity is the hypotenuse of the triangle formed with the horizontal velocity and the vertical velocity. Then:
v0² = v0x² + v0y²
Solving for v0y:
v0y = √(v0² - v0x²)
v0y = √((6.75 m/s)² - (1.65 m/s)²)
v0y = 6.55 m/s
Now, using the equation of the vertical component of the velocity at the maximum height (vy = 0):
vy = v0y + g · t
0 = 6.55 m/s + (-9.8 m/s²) · t
-6.55 m/s / -9.8 m/s² = t
t = 0.67 s
Now, using the equation of the vertical position at t = 0.67 s, we can find the maximum height:
y = y0 + v0y · t + 1/2 · g · t²
y = 0 m + 6.55 m/s · 0.67 s + 1/2 · (-9.8 m/s²) · (0.67 s)²
y = 2.19 m
The maximum height that the fish can jump is 2.19 m.
