Answer:
a. t = 1.43 s
b. d = 7.88 m
Explanation:
a. The time of flight can be found using the following equation:
![y_{f} = y_{0} + v_{0_{y}}t - \frac{1}{2}gt^{2}](https://tex.z-dn.net/?f=%20y_%7Bf%7D%20%3D%20y_%7B0%7D%20%2B%20v_%7B0_%7By%7D%7Dt%20-%20%5Cfrac%7B1%7D%7B2%7Dgt%5E%7B2%7D%20)
Where:
: is the final height = -10 m
: is the initial height = 0
: is the initial speed in the vertical direction = 0
g: is the acceleration due to gravity = 9.81 m/s²
By solving the above equation for "t" we have:
![t = \sqrt{\frac{2y_{f}}{g}} = \sqrt{\frac{2*10 m}{9.81 m/s^{2}}} = 1.43 s](https://tex.z-dn.net/?f=%20t%20%3D%20%5Csqrt%7B%5Cfrac%7B2y_%7Bf%7D%7D%7Bg%7D%7D%20%3D%20%5Csqrt%7B%5Cfrac%7B2%2A10%20m%7D%7B9.81%20m%2Fs%5E%7B2%7D%7D%7D%20%3D%201.43%20s%20)
Hence, the ball will hit the ground in 1.43 s.
b. The distance in the horizontal direction can be found as follows:
![x_{f} = x_{0} + v_{0}t + \frac{1}{2}at^{2}](https://tex.z-dn.net/?f=%20x_%7Bf%7D%20%3D%20x_%7B0%7D%20%2B%20v_%7B0%7Dt%20%2B%20%5Cfrac%7B1%7D%7B2%7Dat%5E%7B2%7D%20)
Where:
x₀: is the initial position in the horizontal direction = 0
a: is the acceleration in the horizontal direction = 0 (it is moving at constant speed)
![x_{f} = 5.51 m/s*1.43 s = 7.88 m](https://tex.z-dn.net/?f=%20x_%7Bf%7D%20%3D%205.51%20m%2Fs%2A1.43%20s%20%3D%207.88%20m%20)
Therefore, the ball will travel 7.88 m before it hits the ground.
I hope it helps you!
Answer:
Height from ground is 8 m where string will break
Explanation:
Let the string makes some angle with the vertical after some instant of time
So here we have
![T - mg cos\theta = \frac{mv^2}{R}](https://tex.z-dn.net/?f=T%20-%20mg%20cos%5Ctheta%20%3D%20%5Cfrac%7Bmv%5E2%7D%7BR%7D)
![T = mg cos\theta + \frac{mv^2}{R}](https://tex.z-dn.net/?f=T%20%3D%20mg%20cos%5Ctheta%20%2B%20%5Cfrac%7Bmv%5E2%7D%7BR%7D)
now by energy conservation we have
![\frac{1}{2}mv^2 = mg(R cos\theta)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20%3D%20mg%28R%20cos%5Ctheta%29)
![mv^2 = 2mgR cos\theta](https://tex.z-dn.net/?f=mv%5E2%20%3D%202mgR%20cos%5Ctheta)
![T = mg cos\theta + 2mgcos\theta](https://tex.z-dn.net/?f=T%20%3D%20mg%20cos%5Ctheta%20%2B%202mgcos%5Ctheta)
![T = 3mg cos\theta](https://tex.z-dn.net/?f=T%20%3D%203mg%20cos%5Ctheta)
For string break down we have
![T = 2mg = 3mgcos\theta](https://tex.z-dn.net/?f=T%20%3D%202mg%20%3D%203mgcos%5Ctheta)
![cos\theta = \frac{2}{3}](https://tex.z-dn.net/?f=cos%5Ctheta%20%3D%20%5Cfrac%7B2%7D%7B3%7D)
Now height from the ground is given as
![h = R - Rcos\theta](https://tex.z-dn.net/?f=h%20%3D%20R%20-%20Rcos%5Ctheta)
![h = 24 - 24(\frac{2}{3})](https://tex.z-dn.net/?f=h%20%3D%2024%20-%2024%28%5Cfrac%7B2%7D%7B3%7D%29)
![h = 8 cm](https://tex.z-dn.net/?f=h%20%3D%208%20cm)
Nuclear fusion reactions convert protons into helium; thus, becoming the source of all energy radiated by the sun.
Answer: Option D
<u>Explanation:</u>
Nuclear fusion reaction is one among the two nuclear reactions in which the atoms nucleus interact with each other to produce the products. In nuclear fusion, two smaller atoms react together to form a new atom with bigger size.
So large amount of energy is required to start the nuclear fusion reaction. The fusion reactions mostly occurs in stars. The illumination in Stars even the Sun is due to nuclear fusion reaction occurring with the atoms present in them.
Mostly the energy radiated by Sun is due to the protons-protons chain reaction. In this chain reaction, the protons get converted into helium due to nuclear fusion reaction, thus becoming the source of all energy radiated by the Sun.
Speed = distance / time
If you input your numbers into this equation you will be able to find the cyclists average speed