Answer:
Time = 1.75[s]; Distance traveled = 21.5 [m]; Max height = 15 [m]
Explanation:
First, we have to break down the velocity vector into the X & y components.
![(v_{x})_{0} = 15 * cos( 35)= 12.28[m/s]\\(v_{y})_{0} = 15 * sin( 35)= 8.6[m/s]\\\\](https://tex.z-dn.net/?f=%28v_%7Bx%7D%29_%7B0%7D%20%3D%2015%20%2A%20cos%28%2035%29%3D%2012.28%5Bm%2Fs%5D%5C%5C%28v_%7By%7D%29_%7B0%7D%20%3D%2015%20%2A%20sin%28%2035%29%3D%208.6%5Bm%2Fs%5D%5C%5C%5C%5C)
To find the time t that lasts the ball of cannon in the air we must use the following equation of kinematics, in this equation the value of y is equal to zero because it will be proposed that the ball lands at the same level that was fired.
![y=(v_{y} )_{0}-\frac{1}{2}*g*t^{2} \\where:\\g=9.81[m/s^2]\\t = time[s]\\y=0[m]](https://tex.z-dn.net/?f=y%3D%28v_%7By%7D%20%29_%7B0%7D-%5Cfrac%7B1%7D%7B2%7D%2Ag%2At%5E%7B2%7D%20%20%20%5C%5Cwhere%3A%5C%5Cg%3D9.81%5Bm%2Fs%5E2%5D%5C%5Ct%20%3D%20time%5Bs%5D%5C%5Cy%3D0%5Bm%5D)
![0=8.6*t-\frac{1}{2}*9.81*t^{2} \\4.905*t^{2}=8.6*t\\ t=1.75[s]](https://tex.z-dn.net/?f=0%3D8.6%2At-%5Cfrac%7B1%7D%7B2%7D%2A9.81%2At%5E%7B2%7D%20%20%5C%5C4.905%2At%5E%7B2%7D%3D8.6%2At%5C%5C%20t%3D1.75%5Bs%5D)
In order to find the distance traveled horizontally from the cannonball, we must use the speed kinematics equation in the X coordinate.
![x = (v_{x})_{0} *t\\x=12.28*1.75\\x=21.5 [m]](https://tex.z-dn.net/?f=x%20%3D%20%28v_%7Bx%7D%29_%7B0%7D%20%20%2At%5C%5Cx%3D12.28%2A1.75%5C%5Cx%3D21.5%20%5Bm%5D)
In order to find the last value, we must bear in mind that when the cannonball reaches the maximum height, the velocity in the component y is equal to zero, and we can find the value of and with the following kinematic equation
![y = (v_{y})_{0} *t+\frac{1}{2} *g*(t)^{2} \\y = 0*t+\frac{1}{2} *9.81*(1.75)^{2}\\ y=15 [m]](https://tex.z-dn.net/?f=y%20%3D%20%28v_%7By%7D%29_%7B0%7D%20%2At%2B%5Cfrac%7B1%7D%7B2%7D%20%2Ag%2A%28t%29%5E%7B2%7D%20%5C%5Cy%20%3D%200%2At%2B%5Cfrac%7B1%7D%7B2%7D%20%2A9.81%2A%281.75%29%5E%7B2%7D%5C%5C%20y%3D15%20%5Bm%5D)
Answer:
The combined gas equation relates three variables pressure, temperature and volume when the number of moles is constant.
The equation is PV / T = constant. Which is valid for a fixed number of moles of the gas.
You can derive the combined gas equation from the combination of Bolye's law, Charles' law and Gay-Lussac's law, which needs some algebra.
Explanation:
The sun, moon, planets and stars rise in the EAST and set in the WEST.
Answer:
The distance traveled by the woman is 34.1m
Explanation:
Given
The initial height of the cliff
yo = 45m final, positition y = 0m bottom of the cliff
y = yo + ut -1/2gt²
u = 20.0m/s initial speed
g = 9.80m/s²
0 = 45.0 + 20×t –1/2×9.8×t²
0 = 45 +20t –4.9t²
Solving quadratically or by using a calculator,
t = 5.69s and –1.61s byt time cannot be negative so t = 5.69s
So this is the total time it takes for the ball to reach the ground from the height it was thrown.
The distance traveled by the woman is
s = vt
Given the speed of the woman v = 6.00m/s
Therefore
s = 6.00×5.69 = 34.14m
Approximately 34.1m to 3 significant figures.
