Two carts with masses of 14.7 kg and 3.2 kg move in opposite directions on a frictionless
horizontal track with speeds of 6.7 m/s and
3.1 m/s, respectively. The carts stick together
after colliding head-on.
Find their final speed.

Speed, V = 4.95m/s

Explanation:

Given the following data;

Mass, M1 = 14.7kg

Mass, M2 = 3.2kg

Velocity, V1 = 6.7m/s

Velocity, V2 = 3.1m/s

To find the final speed;

Mathematically, inelastic collision is given by the formula;

Where;

V is the final velocity in m/s.

M1 is the mass of the first object in kgs.

M2 is the mass of the second object in kgs.

V1 is the initial velocity of the first object in m/s.

V2 is the initial velocity of the second object in m/s.

Substituting into the equation, we have;

Speed, V = 4.95m/s

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