# Physics

Exercise 1:

Three identical particles (P1). (P2), and (P3) are launched from point A, all with the same speed V = 6 m/s but with different launch angles, from the roof of a building of height h = 25 m as shown in the adjacent figure.

The horizontal plane passing through the ground is considered as a gravitational potential energy reference.

Neglect air resistance and take g=10 m/s²

1. The value of the kinetic energy of (P1) at A is KE(P1) = 9 J

1.1 Show that the mass of (P1) is 500g.

1.2. Calculate GPE(P1) the value of the gravitational potential energy of the system [(P1); Earth) at A.

1.3. Deduce that the value of the mechanical energy of the system [(P1); Earth] at A is ME(P1) = 134].

1.4. Determine the speed V1 of (P1) just before reaching the ground at B.

2. Choose with justification the correct answer.

2.1. The kinetic energy of (P1), (P2) and (P3) at A are related such as:

KE(P1) > KE (P2) > KE (P3)

KE(P1)=KE (P2) = KE (P3)

c. KE(P1) <KE (P2) <KE (P3)

2.2 The gravitational potential energy of the system [(P1)arth], [(P2); Earth)] and [(P3); Earth)] at A are related, such as:

a. GPE(P1) > GPE (P2) > GPE (P3)

b. GPE(P) GPE (PL) = GPE (P)

c. GPE(P1) GPE (P2) <GPE (P3)

2.3. The mechanical energy of the system [(P1); Earth], [(P2); Earth)] and [(P3); Earth)] at A are related, such
as:

ME(P1)> ME (P2) > ME (P3)

ME(P1) <ME (P2) <ME (P3)

C. ME(P1)=ME (P2) = ME (P3)

2.4. The speed of the particles (P1); (P2) and (P3) just before reaching the ground at B, C and D are V1; V2 and V3 respectively, and they are related, such as:

a. V1=V2=V3

b. V1<V2<V3

c.V1 > V2 > V3
Exercise 2:

Ahmad throws a ball of mass m=0.1 vertically upwards with speed V0=20 m/s from a point O which is at the height 25 m above the ground . the ball hits point A which is the highest point of its trajectory be found falls to the ground in B.

We take the horizontal plane passing through B as the reference of the gravitational potential energy and we neglect the air resistance, Given:

g=10 m/s²

1) Calculate at point O:

1-1) The kinetic energy of the ball.

1-2) The gravitational potential energy of the system (ball-earth).

1-3) The mechanical energy of the system (ball-earth).

2) 2-1) The mechanical energy of the system (ball-earth) is conserved. Justify.

2.2) Calculate the speed of the ball at point A. Deduce its kinetic energy at A.

2-3) Determine, using the law of conservation of mechanical energy, the gravitational potential energy of the system (ball-earth) at A then deduce the height hA of the ball at A with respect to the ground . 3) Determine the kinetic energy and the velocity VB of the ball at B.