8.854 m/s is the speed of the box after it reaches bottom of the ramp.
<u>Explanation</u>:
From the figure we came to know that height of the block is 4 m.
We know that,
Total "initial energy of an object" = Total "final energy of an object
"
Total "initial energy of an object" is = "sum of potential energy" and "kinetic energy" of an object at its initial position.
![\text { "g" acceleration due to gravity is } 9.8 \mathrm{m} / \mathrm{s}^{2}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20%22g%22%20acceleration%20due%20to%20gravity%20is%20%7D%209.8%20%5Cmathrm%7Bm%7D%20%2F%20%5Cmathrm%7Bs%7D%5E%7B2%7D)
![\text { Total initial energy }=\mathrm{m} \times \mathrm{g} \times \mathrm{h}_{\mathrm{i}}+\frac{1}{2} \mathrm{m} v_{i}^{2}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Total%20initial%20energy%20%7D%3D%5Cmathrm%7Bm%7D%20%5Ctimes%20%5Cmathrm%7Bg%7D%20%5Ctimes%20%5Cmathrm%7Bh%7D_%7B%5Cmathrm%7Bi%7D%7D%2B%5Cfrac%7B1%7D%7B2%7D%20%5Cmathrm%7Bm%7D%20v_%7Bi%7D%5E%7B2%7D)
Initial velocity is “0” as the object does not have starting speed
![\text { Height of the block where the object is placed initially }\left(h_{i}\right) \text { is } 4 \mathrm{m} \text { . }](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Height%20of%20the%20block%20where%20the%20object%20is%20placed%20initially%20%7D%5Cleft%28h_%7Bi%7D%5Cright%29%20%5Ctext%20%7B%20is%20%7D%204%20%5Cmathrm%7Bm%7D%20%5Ctext%20%7B%20.%20%7D)
![\text { Total initial energy }=\mathrm{m} \times 9.8 \times 4+\frac{1}{2} \mathrm{m} 0^{2}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Total%20initial%20energy%20%7D%3D%5Cmathrm%7Bm%7D%20%5Ctimes%209.8%20%5Ctimes%204%2B%5Cfrac%7B1%7D%7B2%7D%20%5Cmathrm%7Bm%7D%200%5E%7B2%7D)
Total initial energy = 39.2 × m
![\text { Total final energy }=\mathrm{m} \times \mathrm{g} \times \mathrm{h}_{\mathrm{f}}+\frac{1}{2} m v_{f}^{2}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Total%20final%20energy%20%7D%3D%5Cmathrm%7Bm%7D%20%5Ctimes%20%5Cmathrm%7Bg%7D%20%5Ctimes%20%5Cmathrm%7Bh%7D_%7B%5Cmathrm%7Bf%7D%7D%2B%5Cfrac%7B1%7D%7B2%7D%20m%20v_%7Bf%7D%5E%7B2%7D)
![\text { We need to find final velocity } v_f](https://tex.z-dn.net/?f=%5Ctext%20%7B%20We%20need%20to%20find%20final%20velocity%20%7D%20v_f)
![\text { Height of the block where the object is travelled to bottom (h_) is } 0 \mathrm{m} \text { . }](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Height%20of%20the%20block%20where%20the%20object%20is%20travelled%20to%20bottom%20%28h_%29%20is%20%7D%200%20%5Cmathrm%7Bm%7D%20%5Ctext%20%7B%20.%20%7D)
![\text { Total final energy }=\mathrm{m} \times 9.8 \times 0+\frac{1}{2} m v_{f}^{2}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Total%20final%20energy%20%7D%3D%5Cmathrm%7Bm%7D%20%5Ctimes%209.8%20%5Ctimes%200%2B%5Cfrac%7B1%7D%7B2%7D%20m%20v_%7Bf%7D%5E%7B2%7D)
Now, Total initial energy of an object = Total final energy of an object
![39.2 \times \mathrm{m}=0.5 \mathrm{m} v_{f}^{2}](https://tex.z-dn.net/?f=39.2%20%5Ctimes%20%5Cmathrm%7Bm%7D%3D0.5%20%5Cmathrm%7Bm%7D%20v_%7Bf%7D%5E%7B2%7D)
![\frac{39.2}{0.5}=v_{f}^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B39.2%7D%7B0.5%7D%3Dv_%7Bf%7D%5E%7B2%7D)
![v_{f}^{2}=78.4](https://tex.z-dn.net/?f=v_%7Bf%7D%5E%7B2%7D%3D78.4)
![v_{f}=\sqrt{78.4}](https://tex.z-dn.net/?f=v_%7Bf%7D%3D%5Csqrt%7B78.4%7D)
![v_{f}=8.854 \mathrm{m} / \mathrm{s}](https://tex.z-dn.net/?f=v_%7Bf%7D%3D8.854%20%5Cmathrm%7Bm%7D%20%2F%20%5Cmathrm%7Bs%7D)
Final speed is 8.854 m/s.
Answer:
<em>faster and at a higher luminosity and temperature.</em>
Explanation:
A protostar looks like a star but its core is not yet hot enough for fusion to take place. The luminosity comes exclusively from the heating of the protostar as it contracts. Protostars are usually surrounded by dust, which blocks the light that they emit, so they are difficult to observe in the visible spectrum.
A protostar becomes a main sequence star when its core temperature exceeds 10 million K. This is the temperature needed for hydrogen fusion to operate efficiently.
Stars above about 200 solar masses (Higher mass) generate power so furiously that gravity cannot contain their internal pressure. These stars blow themselves apart and do not exist for long if at all. A protostar with less than 0.08 solar masses never reaches the 10 million K temperature needed for efficient hydrogen fusion. These result in “failed stars” called brown dwarfs which radiate mainly in the infrared and look deep red in color. They are very dim and difficult to detect, but there might be many of them, and in fact they might outnumber other stars in the universe.
That is why higher mass protostars enter the main sequence at a <em>faster and at a higher luminosity and temperature.</em>
Answer:Same magnitude
Explanation:
When ball is dropped from shoulder height h then velocity at the bottom is given by
![v_1=\sqrt{2gh}](https://tex.z-dn.net/?f=v_1%3D%5Csqrt%7B2gh%7D)
if it makes elastic collision then it will acquire the same velocity and riser up to the same height
If m is the mass of ball then impulse imparted is given by
![J=m(v_2-v_1)](https://tex.z-dn.net/?f=J%3Dm%28v_2-v_1%29)
![J=2m\sqrt{2gh}](https://tex.z-dn.net/?f=J%3D2m%5Csqrt%7B2gh%7D)
Thus impulse imparted by gravity and Floor will have same magnitude of impulse but direction will be opposite to each other.
The middle one on the list is the correct one.
The first one ... distance divided by time ... is Speed, not force.
The third one ... mass times velocity ... is Momentum, not force.