Answer:
his speeds while going to city is 10 mph and while his round trip the speed will be 9 mph
Explanation:
Let say the speed of the bicycle while he moves towards the city is "v"
now the speed of the round trip must be smaller by 1 mph
so its speed for round trip will be
![v_2 = v - 1](https://tex.z-dn.net/?f=v_2%20%3D%20v%20-%201)
now we know that total time of the motion is 19 hr
so we will have
![t_1 = \frac{90}{v}](https://tex.z-dn.net/?f=t_1%20%3D%20%5Cfrac%7B90%7D%7Bv%7D)
![t_2 = \frac{90}{v - 1}](https://tex.z-dn.net/?f=t_2%20%3D%20%5Cfrac%7B90%7D%7Bv%20-%201%7D)
so we will have
![t_1 + t_2 = 19 hr](https://tex.z-dn.net/?f=t_1%20%2B%20t_2%20%3D%2019%20hr)
![\frac{90}{v} + \frac{90}{v-1} = 19](https://tex.z-dn.net/?f=%5Cfrac%7B90%7D%7Bv%7D%20%2B%20%5Cfrac%7B90%7D%7Bv-1%7D%20%3D%2019)
![90(2v - 1) = 19(v^2 - v)](https://tex.z-dn.net/?f=90%282v%20-%201%29%20%3D%2019%28v%5E2%20-%20v%29)
![19 v^2 - 199 v + 90 = 0](https://tex.z-dn.net/?f=19%20v%5E2%20-%20199%20v%20%2B%2090%20%3D%200)
by solving above equation we have
![v = 10 mph](https://tex.z-dn.net/?f=v%20%3D%2010%20mph)
so his speeds while going to city is 10 mph and while his round trip the speed will be 9 mph
Here's what you need to know about waves:
Wavelength = (speed) / (frequency)
Now ... The question gives you the speed and the frequency,
but they're stated in unusual ways, with complicated numbers.
Frequency: How many each second ?
The thing that's making the waves is vibrating 47 times in 26.9 seconds.
Frequency = (47) / (46.9 s) = 1.747... per second. (1.747... Hz)
Speed: How far a point on a wave travels in 1 second.
The crest of one wave travels 4.16 meters in 13.7 seconds.
Speed = (4.16 m / 13.7 sec) = 0.304... m/s
Wavelength = (speed) / (frequency)
Wavelength = (0.304 m/s) / (1.747 Hz) = 0.174 meter per second
Answer:
The speed of the large cart after collision is 0.301 m/s.
Explanation:
Given that,
Mass of the cart, ![m_1 = 300\ g = 0.3\ kg](https://tex.z-dn.net/?f=m_1%20%3D%20300%5C%20g%20%3D%200.3%5C%20kg)
Initial speed of the cart, ![u_1=1.2\ m/s](https://tex.z-dn.net/?f=u_1%3D1.2%5C%20m%2Fs)
Mass of the larger cart, ![m_2 = 2\ kg](https://tex.z-dn.net/?f=m_2%20%3D%202%5C%20kg)
Initial speed of the larger cart, ![u_2=0](https://tex.z-dn.net/?f=u_2%3D0)
After the collision,
Final speed of the smaller cart,
(as its recolis)
To find,
The speed of the large cart after collision.
Solution,
Let
is the speed of the large cart after collision. It can be calculated using conservation of momentum as :
![m_1u_1+m_2u_2=m_1v_1+m_2v_2](https://tex.z-dn.net/?f=m_1u_1%2Bm_2u_2%3Dm_1v_1%2Bm_2v_2)
![m_1u_1+m_2u_2-m_1v_1=m_2v_2](https://tex.z-dn.net/?f=m_1u_1%2Bm_2u_2-m_1v_1%3Dm_2v_2)
![v_2=\dfrac{m_1u_1+m_2u_2-m_1v_1}{m_2}](https://tex.z-dn.net/?f=v_2%3D%5Cdfrac%7Bm_1u_1%2Bm_2u_2-m_1v_1%7D%7Bm_2%7D)
![v_2=\dfrac{0.3\times 1.2+0-0.3\times (-0.81)}{2}](https://tex.z-dn.net/?f=v_2%3D%5Cdfrac%7B0.3%5Ctimes%201.2%2B0-0.3%5Ctimes%20%28-0.81%29%7D%7B2%7D)
![v_2=0.301\ m/s](https://tex.z-dn.net/?f=v_2%3D0.301%5C%20m%2Fs)
So, the speed of the large cart after collision is 0.301 m/s.
Answer: It is a transverse wave ^^
Explanation:
No matter what direction you throw it, or with what speed, its acceleration is immediately 9.8 m/s^2 downward as soon as you release it from your hand, and it doesn't change until the ball hits something.