Answer:
38.4 m/s
Explanation:
a) at t = 3.2s. ![x = 6 * 3.2^2 = 61.44 m](https://tex.z-dn.net/?f=x%20%3D%206%20%2A%203.2%5E2%20%3D%2061.44%20m)
b) at t = 3.2 + Δt. ![x = 6*(3.2 + \Delta t)^2](https://tex.z-dn.net/?f=x%20%3D%206%2A%283.2%20%2B%20%5CDelta%20t%29%5E2)
c) As Δt approaches 0. We can find the velocity by the ratio of Δx/Δt
![v = \frac{\Delta x}{\Delta t} = \frac{x_2 - x_1}{\Delta t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B%5CDelta%20x%7D%7B%5CDelta%20t%7D%20%3D%20%5Cfrac%7Bx_2%20-%20x_1%7D%7B%5CDelta%20t%7D)
![v = \frac{6*(3.2 + \Delta t)^2 - 61.44}{\Delta t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B6%2A%283.2%20%2B%20%5CDelta%20t%29%5E2%20-%2061.44%7D%7B%5CDelta%20t%7D)
![v = \frac{6(3.2^2 + 6.4\Delta t + \Delta t^2) - 61.44}{\Delta t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B6%283.2%5E2%20%2B%206.4%5CDelta%20t%20%2B%20%5CDelta%20t%5E2%29%20-%2061.44%7D%7B%5CDelta%20t%7D)
![v = \frac{61.44 + 38.4\Delta t + \Delta t^2 - 61.44}{\Delta t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B61.44%20%2B%2038.4%5CDelta%20t%20%2B%20%5CDelta%20t%5E2%20-%2061.44%7D%7B%5CDelta%20t%7D)
![v = \frac{\Delta t(38.4 + \Delta t)}{\Delta t}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B%5CDelta%20t%2838.4%20%2B%20%5CDelta%20t%29%7D%7B%5CDelta%20t%7D)
![v = 38.4 + \Delta t](https://tex.z-dn.net/?f=%20v%20%3D%2038.4%20%2B%20%5CDelta%20t)
As Δt approaches 0, v = 38.4 + 0 = 38.4 m/s
Yes potential increases while kinetic decreases
Momentum is conserved when carts are collided on a slanting plane.
To find the answer, we need to know about the conversation of momentum.
<h3>What's the conversation of momentum?</h3>
- Conservation of linear momentum says the total momentum before the collision and after the collision remains the same.
- Mathematically, m1u1+m2u2 = m1v1+m2v2
<h3>How is the momentum conserved when collision occurs on a slanting plane?</h3>
- On a slanting plane, the velocity has two components,
- horizontal component
- horizontal component Vertical component
- So, its momentum has also similar two components.
- The momentum is conserved along horizontal direction and vertical direction separately.
Thus, we can conclude that the momentum is conserved when carts are collided on a slanting plane.
Learn more about the conversation of momentum here:
brainly.com/question/7538238
#SPJ4
Answer:
The final velocity ![\omega_f = 0.4235 \frac{rev}{s}](https://tex.z-dn.net/?f=%5Comega_f%20%3D%200.4235%20%5Cfrac%7Brev%7D%7Bs%7D)
Explanation:
Given data
Mass of merry go round
= 120 kg
Radius = 1.8 m
Initial angular velocity
= 0.6 ![\frac{rev}{sec}](https://tex.z-dn.net/?f=%5Cfrac%7Brev%7D%7Bsec%7D)
Mass of boy
= 25 kg
We know that the final velocity is given by
![\omega_f = \frac{\frac{1}{2}M_m \omega_i }{M_{boy} + \frac{1}{2} M_m }](https://tex.z-dn.net/?f=%5Comega_f%20%3D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7DM_m%20%5Comega_i%20%7D%7BM_%7Bboy%7D%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20M_m%20%7D)
Put all the values in above formula we get
![\omega_f = \frac{\frac{1}{2}(120) 0.6}{25 + \frac{1}{2} (120) }](https://tex.z-dn.net/?f=%5Comega_f%20%3D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%28120%29%20%200.6%7D%7B25%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%28120%29%20%7D)
![\omega_f = 0.4235 \frac{rev}{s}](https://tex.z-dn.net/?f=%5Comega_f%20%3D%200.4235%20%5Cfrac%7Brev%7D%7Bs%7D)
This is the final velocity.