Answer:
Explanation:
(a)
From the given information:
The initial velocity
= 5 m/s
The direction of the angle θ = 30°
Therefore, the component along the x-axis = ![v_1 \ cos \ \theta](https://tex.z-dn.net/?f=v_1%20%5C%20cos%20%5C%20%5Ctheta)
![v_{1 \ x } = 5 \ cos \ 30^0](https://tex.z-dn.net/?f=v_%7B1%20%5C%20x%20%7D%20%3D%205%20%5C%20cos%20%5C%2030%5E0)
![v_{1x} = 4.33 \ m/s](https://tex.z-dn.net/?f=v_%7B1x%7D%20%3D%204.33%20%5C%20m%2Fs)
The component along the y-axis = ![v_2 { \ sin \ \theta}](https://tex.z-dn.net/?f=v_2%20%7B%20%5C%20sin%20%5C%20%20%5Ctheta%7D)
![v_{1 \ y } = 5 \ sin \ 30^0](https://tex.z-dn.net/?f=v_%7B1%20%5C%20y%20%7D%20%3D%205%20%5C%20sin%20%5C%2030%5E0)
![v_{1 \ y } = 2.5 \ m/s](https://tex.z-dn.net/?f=v_%7B1%20%5C%20y%20%7D%20%3D%202.5%20%5C%20m%2Fs)
To find the final velocity( reflected velocity)
using the same magnitude ![v_2 = 5 \ m/s](https://tex.z-dn.net/?f=v_2%20%3D%205%20%5C%20m%2Fs)
The angle from the x-axis can be ![\theta_r = 90^0+60^0](https://tex.z-dn.net/?f=%5Ctheta_r%20%3D%2090%5E0%2B60%5E0)
= 150°
Thus, the component along the x-axis = ![v_2 \ cos \theta _r](https://tex.z-dn.net/?f=v_2%20%20%5C%20cos%20%5Ctheta%20_r)
![v_{2x} = - 0.433 \ m/s](https://tex.z-dn.net/?f=v_%7B2x%7D%20%3D%20-%200.433%20%5C%20m%2Fs)
The component along the y-axis = ![v_2 \ sin \theta_r](https://tex.z-dn.net/?f=v_2%20%5C%20sin%20%5Ctheta_r)
![v_{2y} = 5 \ sin \ 150^0](https://tex.z-dn.net/?f=v_%7B2y%7D%20%3D%205%20%5C%20sin%20%5C%20150%5E0)
![v_{2y} = 2.5 \ m/s](https://tex.z-dn.net/?f=v_%7B2y%7D%20%3D%202.5%20%5C%20m%2Fs)
(b)
The velocity
can be written as in vector form.
![v_1 ^{\to} = v_1 x \hat {i} + v_1 y \hat {j}](https://tex.z-dn.net/?f=v_1%20%5E%7B%5Cto%7D%20%20%3D%20v_1%20x%20%5Chat%20%7Bi%7D%20%2B%20v_1%20y%20%5Chat%20%7Bj%7D)
---- (1)
The reflected velocity in vector form can be computed as:
![v_2 ^{\to} = v_2 x \hat {i} + v_2 y \hat {j}](https://tex.z-dn.net/?f=v_2%20%5E%7B%5Cto%7D%20%20%3D%20v_2%20x%20%5Chat%20%7Bi%7D%20%2B%20v_2%20y%20%5Chat%20%7Bj%7D)
--- (2)
The change in velocity = ![v_2 ^{\to} - v_1 ^{\to}](https://tex.z-dn.net/?f=v_2%20%5E%7B%5Cto%7D%20-%20v_1%20%5E%7B%5Cto%7D)
![\Delta v ^{\to} = - 4.33 \hat i + 2.5 \hat j - 4.33 \hat i - 2.5 \hat j](https://tex.z-dn.net/?f=%5CDelta%20v%20%5E%7B%5Cto%7D%20%3D%20-%204.33%20%5Chat%20i%20%2B%202.5%20%5Chat%20j%20-%204.33%20%5Chat%20i%20-%202.5%20%5Chat%20j)
![\Delta v ^{\to} = - 8.66 \hat { i }](https://tex.z-dn.net/?f=%5CDelta%20v%20%5E%7B%5Cto%7D%20%3D%20-%208.66%20%5Chat%20%20%7B%20i%20%7D)
(c)
The magnitude of change in velocity = ![| \Delta V |](https://tex.z-dn.net/?f=%7C%20%5CDelta%20V%20%7C)
= 8.66 m/s