Explanation:
Find the time it takes for the roadrunner to land.
Given (in the y direction):
Δy = 0 m
v₀ = v sin 10°
a = -9.81 m/s²
Find: t as a function of v
Δy = v₀ t + ½ at²
(0 m) = (v sin 10°) t + ½ (-9.81 m/s²) t²
t = (v sin 10°) / 4.905
Given (in the x direction):
Δx = 20.5 m
v₀ = v cos 10°
a = 0 m/s²
Find: t as a function of v
Δx = v₀ t + ½ at²
(20.5 m) = (v cos 10°) t + ½ (0 m/s²) t²
t = 20.5 / (v cos 10°)
Set equal and solve for v:
(v sin 10°) / 4.905 = 20.5 / (v cos 10°)
v² sin 10° cos 10° = 100.5525
v = 24.2485398301588
Graph:
desmos.com/calculator/x4b2zf1hxj
None of the options shown are correct.
As we know that induced EMF is given by rate of change in magnetic flux
so here we can say
![EMF = \frac{d\phi}{dt}](https://tex.z-dn.net/?f=EMF%20%3D%20%5Cfrac%7Bd%5Cphi%7D%7Bdt%7D)
here we know that
![\phi = BA](https://tex.z-dn.net/?f=%5Cphi%20%3D%20BA)
so here we can say
![EMF = A\frac{dB}{dt}](https://tex.z-dn.net/?f=EMF%20%3D%20A%5Cfrac%7BdB%7D%7Bdt%7D)
![EMF = A\times(\Delta B)\times f](https://tex.z-dn.net/?f=EMF%20%3D%20A%5Ctimes%28%5CDelta%20B%29%5Ctimes%20f)
now by relation of EMF and electric field we can say
![\int E. dl = EMF](https://tex.z-dn.net/?f=%5Cint%20E.%20dl%20%3D%20EMF)
![E. 2 \pi r = \pi r^2 \times(\Delta B)\times f](https://tex.z-dn.net/?f=E.%202%20%5Cpi%20r%20%3D%20%5Cpi%20r%5E2%20%5Ctimes%28%5CDelta%20B%29%5Ctimes%20f)
![E = \frac{r}{2} \times (\Delta B) \times f](https://tex.z-dn.net/?f=E%20%3D%20%5Cfrac%7Br%7D%7B2%7D%20%5Ctimes%20%28%5CDelta%20B%29%20%5Ctimes%20f)
now plug in all values
r = 2.5 cm
![\Delta B = 30.0 - 29.6 = 0.4 T](https://tex.z-dn.net/?f=%5CDelta%20B%20%3D%2030.0%20-%2029.6%20%3D%200.4%20T)
f = 17 Hz
![E = \frac{0.025}{2} \times 0.4 \times 17 = 0.085 V/m](https://tex.z-dn.net/?f=E%20%3D%20%5Cfrac%7B0.025%7D%7B2%7D%20%5Ctimes%200.4%20%5Ctimes%2017%20%3D%200.085%20V%2Fm)
so electric field is given as E = 0.085 N/C
Answer:
E) V=(m/M)v
Explanation:
Given that
Mass of the small ball = m
Initial velocity of the small ball = v
Mass of the larger ball = m
Initial velocity of the larger ball = 0
After the collision
The velocity of the small ball = 0
The velocity of the larger ball = V
There is no any external force that is why linear momentum will be conserve.
From linear momentum conservation
Pi=Pf
m v + M x 0 = m x 0 + M V
m v +0 = 0 + M V
Therefore the answer will be E.
E) V=(m/M)v
Answer:All the forces are acting. The force due to which the car stops that is between road and tire is "friction".
Explanation:
The mercury density (at liquid state) is
![\rho = 13.5 g/cm^3=13500 kg/m^3](https://tex.z-dn.net/?f=%5Crho%20%3D%2013.5%20g%2Fcm%5E3%3D13500%20kg%2Fm%5E3)
And we know that the pressure at the bottom of a column of fluid is given by (Stevin's law)
![p=\rho g h](https://tex.z-dn.net/?f=p%3D%5Crho%20g%20h)
where
![\rho](https://tex.z-dn.net/?f=%5Crho)
is the liquid density
g is the gravitational acceleration
h is the height of the column of fluid
The pressure at the bottom of the beaker is
![p=26000 Pa](https://tex.z-dn.net/?f=p%3D26000%20Pa)
, therefore we can re-arrange the previous equation to get the height of the column of mercury