Answer:
h = 4.04 m
Explanation:
Given that,
Mass of a child, m = 25 kg
The speed of the child at the bottom of the swing is 8.9 m/s
We need to find the height in the air is the child is able to swing. Let the height is h. Using the conservation of energy such that,

Put all the values,

So, the child is able to go at a height of 4.04 m.
Answer:
The angle that the wave would be 
Explanation:
From the question we are told that the opening to the harbor acts just like a single-slit so a boat in the harbor that at angle equal to the second diffraction minimum would be safe and the on at angle greater than the diffraction first minimum would be slightly affected
The minimum is as a result of destructive interference
And for single-slit this is mathematically represented as

where D is the slit with
is the angle relative to the original direction of the wave
m is the order of the minimum j
is the wavelength
Now since in the question we are told to obtain the largest angle at which the boat would be safe
And the both is safe at the angle equal to the second minimum then
The the angle is evaluated as
![\theta = sin ^{-1}[\frac{m\lambda}{D} ]](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20sin%20%5E%7B-1%7D%5B%5Cfrac%7Bm%5Clambda%7D%7BD%7D%20%5D)
Since for second minimum m= 2
The equation becomes

Answer:
v₃ = 5 [m/s]
Explanation:
To solve this problem we must use the definition of linear momentum, which tells us that momentum is equal to the product of mass by Velocity.
P = m*v
where:
P = linear momentum [kg*m/s]
m = mass [kg]
v = velocity [m/s]
We must also clarify that the momentum is preserved i.e. it is equal before the collision and after the collision
Pbeforecollision = Paftercollision
(m₁*v₁) + (m₂*v₂) = (m₁*v₃) + (m₂*v₄)
where:
m₁ = mass of the truck = 3000 [kg]
v₁ = velocity of the truck = 10 [m/s]
m₂ = mass of the car = 1000 [kg]
v₂ = velocity of the car before the collision = 0 (the car is parked)
v₃ = velocity of the truck after the collision [m/s]
v₄ = velocity of the car after the collision = 15 [m/s]
(3000*10) + (1000*0) = (3000*v₃) + (1000*15)
30000 = 3000*v₃ + 15000
3000*v₃ = 30000 - 15000
3000*v₃ = 15000
v₃ = 5 [m/s]
All of the above, work is a measurement of energy transfer, in Joules.
Potential energy = Joules
Kinetic energy = Joules
The key thing here is that anything having to do with just energy or energy transfer is measured in joules.
Answer:
15 m/s
Explanation:
Using the law of conservation of energy, potential energy equals kinetic energy hence

Therefore

where g is the acceleration due to gravity, m is the mass of the object, h is the height and v is the speed of the wallet
Taking g as 9.81 then
