AB is three-fifths the length of AD and BC is three-fifths the length of DE. With the information given above, determine how triangle ABC can be shown to be similar to triangle ADE.

See explanation

Step-by-step explanation:

Given:

- AB = 3/5 * AD

- BC = 3/5 * DE

Find:

Determine how triangle ABC can be shown to be similar to triangle ADE.

Solution:

- The law of similar triangles states that all 3 angles must be similar:

                                 AB / AD = BC / DE = AC / AE

- Then using the given data we will prove the above ratios to be equal:

                                (3/5)*AD / AD = (3/5) BC/BC = 3/5

- Now we know that angle A is common to both triangles ABC and ADE we have sum of angles:

                                 A + B + C = A + D + E

                                      B + C = D + E

- Since, angles B and D lie on parallel lines, the law of corresponding angle states that B = D. Hence,

                                            E = C

- Hence, angle B = D , E = C and angle A is common to both. Proves that both ABC and ADE are similar triangles.

1) Kinetic energy of the truck 1 is 600,000 joules.

Kinetic energy of the truck 2 is 1,837,500 joules.

2 a)Potential energy of truck 1 is 646,800 Joules.

b) Energy lose by the truck 1 just got converted into heat and sound energy during the collision.

Step-by-step explanation:

Mass of the truck 1 and truck 2,m = 3000 kg

Velocity of the truck 1, = = 20 m./s

Velocity of the truck 2, = 35 m./s

1. Kinetic energy of the truck 1:

Kinetic energy of the truck 2:

2.a) Energy loose by the truck 1:

Initial height of the truck on the hill = 22 m

At that height potential energy will be maximum:

Potential energy of truck 1 at that height =

b) Energy lose by the truck 1 just got converted into heat and sound energy during the collision.