A 0.50 kg ball that is traveling at 9.0 m/s collides head-on with a 1.00 kg ball moving in the opposite direction at a speed of 11.0 m/s. The 0.50 kg ball bounces backward at 15.0 m/s after the collision. Find the speed of the second ball after the collision.

1 m/s

Explanation:

From the law of conservation of momentum,

Total momentum before collision = Total momentum after collision

mu + m'u' = mv + m'v' Equation 1

Where m = mass of the first ball m' = mass of the second ball, u = initial velocity of the first ball, u' = initial velocity of the second ball, v = final velocity of the first ball, v' = final velocity of the second ball.

Note: Let the direction of the first ball be positive.

Given: m = 0.5 kg, u = 9.0 m/s, m' = 1 kg, u' = - 11 m/s ( opposite direction to the first ball), v = - 15 m/s ( bounces backward).

Substitute into equation 1

0.5(9) + 1(-11) = 0.5(-15) + 1(v')

Solving for v'

4.5-11 = -7.5 + v'

-6.5 = -7.5 + v'

v' = 7.5-6.5

v' = 1 m/s.

Hence the speed of the second ball after collision = 1 m/s

since you're a real machine, your ama is always less than your ima, because you can never totally eliminate friction.

emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50