Carlos is baking a cake. The last step in the directions is to put the cake batter in the oven. Why does Carlos need to put the
2 answers:
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Answer:
.
Explanation:
When the ball is placed in this pool of water, part of the ball would be beneath the surface of the pool. The volume of the water that this ball displaced is equal to the volume of the ball that is beneath the water surface.
The buoyancy force on this ball would be equal in magnitude to the weight of water that this ball has displaced.
Let denote the mass of this ball. Let
denote the mass of water that this ball has displaced.
Let denote the gravitational field strength. The weight of this ball would be
. Likewise, the weight of water displaced would be
.
For this ball to stay afloat, the buoyancy force on this ball should be greater than or equal to the weight of this ball. In other words:
.
At the same time, buoyancy is equal in magnitude the the weight of water displaced. Thus:
.
Therefore:
.
.
In other words, the mass of water that this ball displaced should be greater than or equal to the mass of of the ball. Let denote the density of water. The volume of water that this ball should displace would be:
.
Given that while
:
.
In other words, for this ball to stay afloat, at least of the volume of this ball should be under water. Therefore, the volume of this ball should be at least
.
Answer:
D.
Explanation:
In order to know how long after Bill released his rock should Ted throw his if they want the stones to hit the water simultanously, we need to calculate the time needed to hit the water to both rocks independent each other, and just take the difference.
For the rock dropped by Bill, as the only influence on it is gravity (accelerating it downwards with an acceleration equal to g), and v₀ =0, we can use the following kinematic equation:
where y = height = 40 ft.
As all the parameters are given in SI units, it is advisable to convert this value to m, as follows:
Now, we can solve for t, as follows:
For the rock thrown down at 10 m/s, the kinematic equation we just have used becomes:
This leaves us a quadratic equation on t, as follows:
Taking the positive root, we have:
t = -1.02 s + 1.88 s = 0.86 s
So, in order to get that both rocks hit the water at the same time, Ted will need to wait the difference between both times:
Δt = 0.86 s - 1.58s = -0.72 s