Respuesta :
Answer:
a) v(0.3) = ( 8, 0 , 9.943 )
b) 21.1 m/s
c) S(0.5) = (4, 9.5 , 9.72625)
Explanation:
s(0) = 8i + 0j -7k
v(0) = -8i +19j -3k
a(t) = (0i+0j-9.81k)
part a
v(t) = v(0) + a(t)*t
v(0.3) = 8i + 0j -7k + (0i+0j-9.81k)* 0.3
v(0.3) = 8i + 0j - 9.943k
part b
S(t) = s(0) + v(0)*t + 0.5*a(t)*t^2
S(0.3) - S (0) = v(0)*t + 0.5*a(t)*t^2
= (-8i +19j -3k)*0.3 + 0.5*(0i+0j-9.81k)*(0.3)^2
= (-2.4i + 5.7j - .9k) + (0i+0j-0.44145k)
Displacement = (-2.4i + 5.7j - 1.34145k)
[tex]distance = \sqrt{2.4^2+5.7^2+1.34145^2}\\ = 6.3285 m[/tex]
Average velocity = 6.3285 / 0.3 = 21.1 m/s
part c
S(t) = s(0) + v(0)*t + 0.5*a(t)*t^2
S(0.5) = v(0)*t + 0.5*a(t)*t^2 + S(0)
=(-8i +19j -3k)*0.5 + 0.5*(0i+0j-9.81k)*(0.5)^2 + (8i + 0j -7k)
=(-4i + 9.5j - 1.5k) + (0i+0j-1.22625k) + (8i + 0j -7k)
=(4i + 9.5j - 9.72625k)
In this exercise we have to use the knowledge of vectors to calculate the speed of the ball, so:
A) [tex]v(0.3) = ( 8, 0 , 9.943 )[/tex]
B) [tex]21.1 m/s[/tex]
C) [tex]S(0.5) = (4, 9.5 , 9.72625)[/tex]
Given the following information about the equations we have:
- [tex]s(0) = 8i + 0j -7k[/tex]
- [tex]v(0) = -8i +19j -3k[/tex]
- [tex]a(t) = 0i+0j-9.81k[/tex]
A)So calculating the speed of the ball, we have:
[tex]v(t) = v(0) + a(t)*t\\v(0.3) = 8i + 0j -7k + (0i+0j-9.81k)* 0.3\\v(0.3) = 8i + 0j - 9.943k[/tex]
B) So calculating the average velocity we have:
[tex]S(t) = s(0) + v(0)*t + 0.5*a(t)*t^2\\S(0.3) - S (0) = v(0)*t + 0.5*a(t)*t^2\\= (-8i +19j -3k)*0.3 + 0.5*(0i+0j-9.81k)*(0.3)^2\\= (-2.4i + 5.7j - .9k) + (0i+0j-0.44145k)\\= 6.3285 / 0.3 = 21.1 m/s[/tex]
C) Then calculating the average velocity of the ball in 0.5 seconds, we find that:
[tex]S(t) = s(0) + v(0)*t + 0.5*a(t)*t^2\\S(0.5) = v(0)*t + 0.5*a(t)*t^2 + S(0)\\=(-8i +19j -3k)*0.5 + 0.5*(0i+0j-9.81k)*(0.5)^2 + (8i + 0j -7k)\\=(-4i + 9.5j - 1.5k) + (0i+0j-1.22625k) + (8i + 0j -7k)\\=(4i + 9.5j - 9.72625k)[/tex]
See more about vectores at brainly.com/question/13188123
