3.01 m/s
This is a simple projectile calculation. What we want is a vertical velocity such that the time the droplet spends going up and going back down to the surface exactly matches the time the droplet takes to travel horizontally 0.800 meters. The time the droplet spends in the air will is:
V*sqrt(3)/2 ; Vertical velocity.
(V*sqrt(3)/2)/9.8 ; Time until droplet reaches maximum height
(V*sqrt(3))/9.8 ; Double that time for droplet to fall back to the surface.
The droplet's horizontal velocity will be:
V/2.
So the total distance the droplet travels will be:
d = (V*sqrt(3))/9.8 * V/2
d = V^2*sqrt(3)/19.6
Let's substitute the desired distance and solve for V
d = V^2*sqrt(3)/19.6
0.8 = V^2*sqrt(3)/19.6
15.68 = V^2*sqrt(3)
15.68/sqrt(3) = V^2
15.68/1.732050808 = V^2
3.008795809 = V
So after rounding to 3 significant figures, the archerfish needs to spit the water at a velocity of 3.01 m/s
Let's verify that answer.
Vertical velocity: 3.01 * sin(60) = 3.01 * 0.866025404 = 2.606736465
Time of flight = 2.606736465 * 2 / 9.8 = 0.531987034 seconds.
Horizontal velocity: 3.01 * cos(60) = 3.01 * 0.5 =
Answer: 17000000 ounces of gold were mined in that country that year.
Step-by-step explanation:
Let x represent the number of ounces of gold that were mined in that country that year.
Approximately 1,870,000 oz of gold went into the manufacturing of electronic equipment in a certain country in 1 year. This was 11% of all the gold mined in that country that year. This means that
11/100 × x = 1870000
0.11x = 1870000
x = 1870000/0.11
x = 17000000
The area of a Triangle is 1/2BH (B=Base length, H=Height)
When looking at the points, we can figure out the following:
The distance between the two points at the base is 8 (to get from -4 to 4 you must add 8) and the height is 4 (to get from -4 to 0 as well as 0 to 4, the distance is 4).
Now we plug in our values:
Area= 1/2(8)(4)
=1/2(32)
=16 Units squared
Therefore, your answer is 16 units squared.
I hope this Helps!
-Sinnamin
Answer:
Please see the attached picture for full solution.
