9514 1404 393
Answer:
1.114 kg/m³
Explanation:
The total mass of the air in the balloon and the balloon + cargo will be the mass of the displaced air. If d is the density of the air in the balloon, then we have ...
2910d +308 = 2910×1.22
Solving for d, we find ...
2910d = 2919(1.22) -308
d = 1.22 -308/2910
d ≈ 1.114 . . . kg/m³
The density of the hot air is about 1.114 kg/m³.
Answer:
At the closest point
Explanation:
We can simply answer this question by applying Kepler's 2nd law of planetary motion.
It states that:
"A line connecting the center of the Sun to any other object orbiting around it (e.g. a comet) sweeps out equal areas in equal time intervals"
In this problem, we have a comet orbiting around the Sun:
- Its closest distance from the Sun is 0.6 AU
- Its farthest distance from the Sun is 35 AU
In order for Kepler's 2nd law to be valid, the line connecting the center of the Sun to the comet must move slower when the comet is farther away (because the area swept out is proportional to the product of the distance and of the velocity: , therefore if r is larger, then v (velocity) must be lower).
On the other hand, when the the comet is closer to the Sun the line must move faster (, if r is smaller, v must be higher). Therefore, the comet's orbital velocity will be the largest at the closest distance to the Sun, 0.6 A.
Answer:
27.3 m/s
Explanation:
We are given that
Distance travel by ball=x=60 m
We have to find the initial speed( of the ball.
Using the formula
The value of y at point of foot of the vertical distance
y=0
Using
Using the formula
Hence, the initial speed of the ball=27.3 m/s
I'll just find out the path difference between the waves at the starting point. At infinity, the path difference will be zero because the observer will be infinitely far away from both. As the observer goes farther, the path difference keeps reducing till it reaches zero as the observer reaches infinity.
<span>Path difference at starting point = Distance from lower speaker - Distance from upper speaker = √((3)² + (2.5)²) - 2.5 = 1.405 m </span>
<span>Now to find wavelength. </span>
<span>Speed of sound in air at 20 degrees C = 343 m/s </span>
<span>Wavelength = 343 / 686 = 0.5 m </span>
<span>Destructive interference occurs when path difference = (2n + 1)λ/2 where n is an integer. </span>
<span>Maximum n possible can be found by, </span>
<span>(2n + 1)λ/2 < 1.405 </span>
<span>(2n + 1) < (1.4)(2) / (0.5) </span>
<span>2n < 5.6 - 1 </span>
<span>2n < 4.6 </span>
<span>n < 2.3 </span>
<span>So, we have 3 values of n, 0, 1 and 2. </span>
<span>Path differences are, λ/2, 3λ/2 and 5λ/2 which have values 0.25 m , 0.75 m and 1.25 m </span>
<span>But the question asks for distance from starting point. (sheesh!!) </span>
<span>Lets say the observer walked x distance. </span>
<span>Path difference = √((3)² + (2.5 + x)²) - (2.5 + x) </span>
<span>Equate this expression to the values obtained above to get the different values of x. </span>