Answer:
Explanation:
Given
inclination ![\theta =30^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%20%3D30%5E%7B%5Ccirc%7D)
initial speed ![u=20\ m/s](https://tex.z-dn.net/?f=u%3D20%5C%20m%2Fs)
Point of release is 45 m above the ground
Considering stone to be a projectile, so time taken by projectile for its zero vertical displacement is
![t_1=\frac{2u\sin \theta }{g}](https://tex.z-dn.net/?f=t_1%3D%5Cfrac%7B2u%5Csin%20%5Ctheta%20%7D%7Bg%7D)
![t_1=\frac{2\times 20\times \sin 30}{10}](https://tex.z-dn.net/?f=t_1%3D%5Cfrac%7B2%5Ctimes%2020%5Ctimes%20%5Csin%2030%7D%7B10%7D)
![t_1=2\ s](https://tex.z-dn.net/?f=t_1%3D2%5C%20s)
Now after completing zero vertical displacement , stone needs to travel another 45 m in downward direction with initial speed u=20\sin 30
![h=u_yt+\frac{1}{2}a_yt^2](https://tex.z-dn.net/?f=h%3Du_yt%2B%5Cfrac%7B1%7D%7B2%7Da_yt%5E2)
where, ![h=height](https://tex.z-dn.net/?f=h%3Dheight)
![u_y=vertical velocity](https://tex.z-dn.net/?f=u_y%3Dvertical%20velocity)
![a_y=vertical acceleration](https://tex.z-dn.net/?f=a_y%3Dvertical%20acceleration)
![t_0=time](https://tex.z-dn.net/?f=t_0%3Dtime)
![45=20\sin 30+\frac{1}{2}(9.8)(t_0)^2](https://tex.z-dn.net/?f=45%3D20%5Csin%2030%2B%5Cfrac%7B1%7D%7B2%7D%289.8%29%28t_0%29%5E2)
![t_0^2=\frac{70}{9.8}](https://tex.z-dn.net/?f=t_0%5E2%3D%5Cfrac%7B70%7D%7B9.8%7D)
![t_0=2.64\ s](https://tex.z-dn.net/?f=t_0%3D2.64%5C%20s)
thus total time time required is ![t=t_0+t_1=2.64+2=4.64\ s](https://tex.z-dn.net/?f=t%3Dt_0%2Bt_1%3D2.64%2B2%3D4.64%5C%20s)
vertical velocity just before hitting
![v_y=\sqrt{u_y^2+2\times a_y\times s}](https://tex.z-dn.net/?f=v_y%3D%5Csqrt%7Bu_y%5E2%2B2%5Ctimes%20a_y%5Ctimes%20s%7D)
![v_y=\sqrt{10^2+2\times 10\times 45}](https://tex.z-dn.net/?f=v_y%3D%5Csqrt%7B10%5E2%2B2%5Ctimes%2010%5Ctimes%2045%7D)
![v_y=\sqrt{1000}=31.622\ m/s](https://tex.z-dn.net/?f=v_y%3D%5Csqrt%7B1000%7D%3D31.622%5C%20m%2Fs)
Horizontal velocity ![v_x=u\cos 30=17.32\ m/s](https://tex.z-dn.net/?f=v_x%3Du%5Ccos%2030%3D17.32%5C%20m%2Fs)
Net velocity Just before hitting ![=\sqrt{v_x^2+v_y^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7Bv_x%5E2%2Bv_y%5E2%7D)
![=\sqrt{(17.32)^2+(31.62)^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%2817.32%29%5E2%2B%2831.62%29%5E2%7D)
![=\sqrt{1299.82}=36.05\ m/s](https://tex.z-dn.net/?f=%3D%5Csqrt%7B1299.82%7D%3D36.05%5C%20m%2Fs)
Answer:
A) θ = 13.1º , B) E
Explanation:
A) For this exercise, let's use Newton's second law, let's set a reference frame where the axis ax is in the radial direction and is horizontal, the axis y is vertical.
In this reference system the only force that we must decompose is the Normal one, let's use trigonometry
sin θ = Nₓ / N
cos θ =
/ N
Nₓ = N sin θ
Ny = N cos θ
x-axis (radial)
Nₓ = m a
where the acceleration is centripetal
a = v² / R
we substitute
-N sin θ = -m v² / R (1)
the negative sign indicates that the force and acceleration towards the center of the circle
y-axis (Vertical)
Ny - W = 0
N cos θ = mg
N = mg / cos θ
we substitute in 1
mg / cos θ sin θ = m v² / R
g tan θ = v² / R
θ = tan⁻¹ (v² / gR)
we calculate
θ = tan⁻¹ (25² / 9.8 274)
θ = 13.1º
B) when comparing the equations the correct one is E
Answer:
<em>In the case of a solar thermal panel we are trying to heat above the ambient temperature so conduction and convection will work against us by taking heat from the panel to the out- side world. ... The sun (at 6000 C surface temperature) is hotter than the solar panel so the panel will get hot due to the solar radiation.</em>
Explanation:
Answer: 3 H
An acid consists of a hydrogen {positive radical} and a halogen or negative radical. When it is dissolved in water, the ionic bond is broken and ions are separated. The free H+ radical gets attracted to Hydrogen of water H2O and so it forms H3O+. The ionic bond gets weaker in water as electromagnetic forces are weak in water as water is dielectric medium.
Answer:
N = 1364 N
Explanation:
given data
accelerate upward = 5.70 m/s²
mass = 88.0 kg
solution
normal force is in upward direction so, weight of the student in downward direction and acceleration is in upward direction so formula is express as
N - mg = ma ...........................1
N = m × (g+a)
put here value
N = 88.0 × (9.8 + 5.70)
N = 1364 N