Aball is kicked from a location < 8, 0, -7> (on the ground) with initial velocity < -8, 19, -3> m/s. the ball's speed is low enough that air resistance is negligible.(a) what is the velocity of the ball 0.3 seconds after being kicked? (use the momentum ) what is the average velocity of the ball over this time interval? (c) use the average velocity to find the location of the ball 0.5 seconds after being kicked.

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)

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)

answer: a) y=-8x+5

a) m= -8

b) m= -2

c) m= 7

d) m= 6