The sphere will go up until all the initial kinetic energy be transformed into potential energy.
Intital kinetic energy = m*(vi)^2 / 2
Final potential energy = mgh
mgh = m(vi)^2 / 2 => h = (vi)^2 / (2g)
g = 9.81 m/s^2
vi = (1.5m/s)^2
h = (1.5m/s)^2 / (2*9.81m/s)^2 = 0.115 m
The range is the distance run over the ramp
Using trigonometry, sin(20°) = h /run => run = h / sin(20) = 0.115m / sin(20) = 0.336 m
Answer: 0.336 m
The initial speed of the ball is 5 m/s
Explanation:
We can solve the problem by using the law of conservation of momentum: in absence of external forces, the total momentum of the skater + ball system must be conserved. So we can write:
![p_i = p_f](https://tex.z-dn.net/?f=p_i%20%3D%20p_f)
![mu=(m+M)V](https://tex.z-dn.net/?f=mu%3D%28m%2BM%29V)
where:
m = 5 kg is the mass of the ball
u is the initial velocity of the ball
M = 45 kg is the mass of the ice skater
V = 0.5 m/s is the final velocity of the skater+ball together
Solving for u, we can find the initial velocity of the ball:
![u=\frac{m+M}{m}V=\frac{5+45}{5}(0.5)=5 m/s](https://tex.z-dn.net/?f=u%3D%5Cfrac%7Bm%2BM%7D%7Bm%7DV%3D%5Cfrac%7B5%2B45%7D%7B5%7D%280.5%29%3D5%20m%2Fs)
Learn more about momentum:
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Answer:
His kinetic energy increases, potential energy decreases
The sum of kinetic and potential energy is a constant at any instant before he comes to rest.
Explanation:
Snowboarder is starting from a height and moving to the down direction. As he moves down his velocity increases, we know that kinetic energy is given by the expression
, so as he moves his kinetic energy increases.
When the snowboarder is starting his potential energy is maximum(Potential energy = mgh), as he comes down his potential energy decreases.
Based on this we can conclude that the sum of potential energy and kinetic energy is a constant at any instant for a snowboarder before he comes to rest.
mgh+
= Constant
Density = Mass per unit Volume
that is,
D = m / V
Now,
We've been provided with,
Density = 790 kg/m³
Volume = 1250 litres = 1.250 m³
Now,
![density = \frac{mass}{volume} \\ 790 = \frac{m}{1.250} \\ 790 \times 1.250 = m \\ m = 790 \times 1.250 \\ m = 790 \times \frac{1250}{1000} \\ m = 790 \times \frac{5}{4} \\ m = 197.5 \times 5 \\ m = \frac{1975}{10} \times 5 \\ m = \frac{1975}{2} = 987.5 \: kg](https://tex.z-dn.net/?f=density%20%3D%20%5Cfrac%7Bmass%7D%7Bvolume%7D%20%5C%5C%20790%20%3D%20%5Cfrac%7Bm%7D%7B1.250%7D%20%5C%5C%20790%20%5Ctimes%201.250%20%3D%20m%20%5C%5C%20m%20%3D%20790%20%5Ctimes%201.250%20%5C%5C%20m%20%3D%20790%20%5Ctimes%20%5Cfrac%7B1250%7D%7B1000%7D%20%5C%5C%20m%20%3D%20790%20%5Ctimes%20%5Cfrac%7B5%7D%7B4%7D%20%5C%5C%20m%20%3D%20197.5%20%5Ctimes%205%20%5C%5C%20m%20%3D%20%5Cfrac%7B1975%7D%7B10%7D%20%5Ctimes%205%20%5C%5C%20m%20%3D%20%5Cfrac%7B1975%7D%7B2%7D%20%3D%20987.5%20%5C%3A%20kg)
987.5 kg of mass will a 1250 litres tank will hold.
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Answer:the molecules begin to collide with each other.
Explanation:
When the temperature of the ground increases the movement of the molecules in the ground also increases due to their collision with each other.