Answer:
Inverse Square Law Newton proposed the Inverse Square Law. The effect of gravity (and also on forces such as sunlight) works like this. If say we have a half-mass Earth, it would produce a gravity of not half but a quarter (the square of 2).
Answer : The final temperature is, 
Explanation :
In this problem we assumed that heat given by the hot body is equal to the heat taken by the cold body.
where,
= specific heat of ice = 
= specific heat of water = 
= mass of ice = 50 g
= mass of water = 200 g
= final temperature = ?
= initial temperature of ice = 
= initial temperature of water = 
Now put all the given values in the above formula, we get:
Therefore, the final temperature is,
Answer:
vb = 22.13 m/s
So, the only thing that was measured here was the height of point A relative to point B. And the Law of Conservation of Energy was used.
Explanation:
In order to find the speed of roller coaster at Point B, we will use the law of conservation of Energy. In this situation, the law of conservation of energy states that:
K.E at A + P.E at A = K.E at B + P.E at B
(1/2)mvₐ² + mghₐ = (1/2)m(vb)² + mg(hb)
(1/2)vₙ² + ghₐ = (1/2)(vb)² + g(hb)
where,
vₙ = velocity of roller coaster at point a = 0 m/s
hₙ = height of roller coaster at point a = 25 m
g = 9.8 m/s²
vb = velocity of roller coaster at point B = ?
hb = Height of Point B = 0 m (since, point is the reference point)
Therefore,
(1/2)(0 m/s)² + (9.8 m/s²)(25 m) = (1/2)(vb)² + (9.8 m/s²)(0 m)
245 m²/s² * 2 = vb²
vb = √(490 m²/s²)
<u>vb = 22.13 m/s</u>
<u>So, the only thing that was measured here was the height of point A relative to point B. And the Law of Conservation of Energy was used.</u>
The sound wave will have traveled 2565 m farther in water than in air.
Answer:
Explanation:
It is known that distance covered by any object is directly proportional to the velocity of the object and the time taken to cover that distance.
Distance = Velocity × Time.
So if time is kept constant, then the distance covered by a wave can vary depending on the velocity of the wave.
As we can see in the present case, the velocity of sound wave in air is 343 m/s. So in 2.25 s, the sound wave will be able to cover the distance as shown below.
Distance = 343 × 2.25 =771.75 m
And for the sound wave travelling in fresh water, the velocity is given as 1483 m/s. So in a time interval of 2.25 s, the distance can be determined as the product of velocity and time.
Distance = 1483×2.25=3337 m.
Since, the velocity of sound wave travelling in fresh water is greater than the sound wave travelling in air, the distance traveled by sound wave in fresh water will be greater.
Difference in distance covered in water and air = 3337-772 m = 2565 m
So the sound wave will have traveled 2565 m farther in water than in air.
Answer: 288.8 m
Explanation:
We have the following data:
is the time it takes to the child to reach the bottom of the slope
is the initial velocity (the child started from rest)
is the angle of the slope
is the length of the slope
Now, the Force exerted on the sled along the ramp is:
(1)
Where 
is the mass of the sled and 
its acceleration
In addition, if we draw a free body diagram of this sled, the force along the ramp will be:
(2)
Where 
is the acceleration due gravity
Then:
(3)
Finding :
(4)
(5)
(6)
Now, we will use the following kinematic equations to find :
(7)
(8)
Where 
is the final velocity
Finding from (7):
(9)
(10)
Substituting (10) in (8):
(11)
Finding :
