1. Alexandra and Rachel are on a train that sounds a whistle at a constant frequency as
2 answers:
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Answer:
Explanation:
For this problem to be easier to calculate, we can represent the triangle as a right triangle whose right angle is located at the origin of a coordinate system. (See picture attached).
With this disposition of the triangle, we can start finding our integral. The hydrostatic force can be set as an integral with the following shape:
γhxdy
we know that γ=62.5 lb/
from the drawing, we can determine the height (or depth under the water) of each differential area is given by:
h=8-y
x can be found by getting the equation of the line, which we'll get by finding the slope of the line and using one of the points to complete the equation:
when substituting the x and y-values given on the graph, we get that the slope is:
once we got this slope, we can substitute it in the point-slope form of the equation:
which yields:
which simplifies to:
we can now solve this equation for x, so we get that:
with this last equation, we can substitute everything into our integral, so it will now look like this:
Now that it's all written in terms of y we can now simplify it, so we get:
we can now proceed and evaluate it.
When using the power rule on each of the terms, we get the integral to be:
By using the fundamental theorem of calculus we get:
When solving we get:
Answer:
t=2.10 s
u= 47.40 m/s
Explanation:
given that
h= 21.8 m
x= 101 m
g=9.8 m/s²
Lets take horizontal speed of ball = u m/s
The vertical speed of the car at initial condition is zero ( v= 0).
We know that
v= 0 m/s
now by putting the values
21.8 = 1/2 x 9.8 x t²
t=2.10 s
This is time when ball was in motion.
Now in horizontal direction
x = u .t
101 = u x 2.1
u= 47.40 m/s