Answer: (d)
Explanation:
Given
Mass of the first ram 
The velocity of this ram is 
Mass of the second ram 
The velocity of this ram 
They combined after the collision
Conserving the momentum
![\Rightarrow m_1v_1+m_2v_2=(m_1+m_2)v\\\Rightarrow 49\times (-7)+52\times (9)=(52+49)v\\\Rightarrow v=\dfrac{125}{101}\ m/s \quad[\text{east}]](https://tex.z-dn.net/?f=%5CRightarrow%20m_1v_1%2Bm_2v_2%3D%28m_1%2Bm_2%29v%5C%5C%5CRightarrow%2049%5Ctimes%20%28-7%29%2B52%5Ctimes%20%289%29%3D%2852%2B49%29v%5C%5C%5CRightarrow%20v%3D%5Cdfrac%7B125%7D%7B101%7D%5C%20m%2Fs%20%5Cquad%5B%5Ctext%7Beast%7D%5D)
Momentum after the collision will be
Therefore, option (d) is correct
Explanation:
There are many ways to achieve a healthier lifestyle and increase fitness. Healthy eating and constant exercise are essential for maintaining good physical and mental health. Through effective nutrition the human body is able to function better, there is an increase in disposition, improvement in immunity, improvement in blood rates, etc. Physical exercise, on the other hand, assists in strengthening muscles, controlling blood pressure, preventing cardiovascular disease, greater satisfaction, less stress, etc.
Some simple examples that can assist in improving health and fitness are:
- Reduction of processed foods, sugars and soft drinks.
- Increased fiber intake
- Daily walks of at least 30 minutes
- Increased water consumption
- Increased consumption of fruits and vegetables
- Incorporate meditation and yoga practices
Answer:
95 J
Explanation:
You can calculate efficiency by dividing useful output by total input, then multiplying it to 100.
So the foumula goes like:
Efficiency= (Useful output/Total input)x100
In this question,
Efficiency= 95%
Useful output= x
Total input= 200
Therefore;
95=(x/200)x100
0.95=x/100
x=0.95x100
x=95 Joules
Answer:
V is approximately = 23m/s
Explanation:
Kinetic energy = ½ mv²
Where m= mass = 0.450kg
V= velocity =?
K. E = 119J
Therefore
K. E = ½ mv²
Input values given
119= ½ × 0.450 × v²
Multiply both sides by 2
119 ×2 = 2 × 1/2 × 0.450 × v²
238= 0.450v²
Divide both sides by 0.450
238/0.450 = 0.450v²/0.450
v² = 528.89
Square root both sides
Sq rt v² = sq rt 528.89
V = 22.998m/s
V is approximately = 23m/s
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Answer:
a)
Y0 = 0 m
Vy0 = 15 m/s
ay = -9.81 m/s^2
b) 7.71 m
c) 3.06 s
Explanation:
The knowns are that the initial vertical speed (at t = 0 s) is 15 m/s upwards. Also at that time the dolphin is coming out of the water, so its initial position is 0 m. And since we can safely assume this happens in Earth, the acceleration is the acceleration of gravity, which is 9.81 m/s^2 pointing downwards
Y(0) = 0 m
Vy(0) = 15 m/s
ay = -9.81 m/s^2 (negative because it points down)
Since acceleration is constant we can use the equation for uniformly accelerated movement:
Y(t) = Y0 + Vy0 * t + 1/2 * a * t^2
To find the highest point we do the first time derivative (this is the speed:
V(t) = Vy0 + a * t
We equate this to zero
0 = Vy0 + a * t
0 = 15 - 9.81 * t
15 = 9.81 * t
t = 0.654 s
At this time it will have a height of:
Y(0.654) = 0 + 15 * 0.654 - 1/2 * 9.81 * 0.654^2 = 7.71 m
The doplhin jumps and falls back into the water, when it falls again it position will be 0 again. So we can equate the position to zero to find how long it was in the air knowing that it started the jump at t = 0s.
0 = Y0 + Vy0 * t + 1/2 * a * t^2
0 = 0 + 15 * t - 1/2 * 9.81 t^2
0 = 15 * t - 4.9 * t^2
0 = t * (15 - 4.9 * t)
t1 = 0 This is the moment it jumped into the air
0 = 15 - 4.9 * t2
15 = 4.9 * t2
t2 = 3.06 s This is the moment when it falls again.
3.06 - 0 = 3.06 s
