Exercise 2.1 Linear MotionFree fall under gravity without air resistance

Q1 An object is placed 3.0 m above the ground. It is thrown vertically downwards at a speed of 2.0 ms-1. Determinea) the time taken by the object to reach the groundb) the speed at the moment the object hits the ground( Assume g =10 ms-2)( Answer a) t= 0.6 s, b) v= 8.0 ms-1 )( Assumption= direction s,v,g pointing downward is +)

Vertical motion upwards without air resistance

Q2 A piece of stone is thrown from the ground vertically upwards at a speed of 30 ms-1. Determine the time interval between two instances when the stone is at the same height of 25 m above the ground.( Assume g =10 ms-2)( Answer ; t= 1.0 s or 5.0 s. So the time interval is 4.0 s )

Q3. An object is thrown vertically upwards from the flat roof of a building at a speed of 15 ms-1. The object reaches the ground after 4.0 s. Determine a) the height of the buildingb) the velocity of the object when it reaches the ground( Assume g =10 ms-2)( Answer ; a)s= -20 m, so the height of the building is 20 m, b) v = - 25 ms-1 (– indicates the direction of velocity is pointing downward))

Q4. An object is thrown vertically upwards at a speed of 20 ms-1 from a point P, 25 m above the ground. Sketcha) Dispalcement-time graphb) a velocity- time graphc) A speed-time graphfor the motion of the object. Use s= 0 at point P( Anwer; a) H= 20 m, b)t= 4.0 s , c)t= 5.0 s, )

Q5. A ball is thrown vetically upwards from the top of a building at a speed of 15 ms-1. If the height of the building is 200 m, determinea) the time taken by the ball to reach the groundb) the velocity when the ball reaches the ground( Answer :a) 8 s, b) v= - 65 ms-1 )

Q6 An object is thrown vertically upwards at a speed of 40 ms-1. Determine a) the time taken by the object to reach the maximum heightb) the maximum height reachedc) the velocity 2.0 s after throwing the objectd) the velocity 6.0 s after throwing the object( Answer; a) t= 4.0 s, b)s= 80 m, c) v= 20 ms-1 directed upwards, v= -20 ms-1 downwards)Q7. An object is thrown vertically upwards from the ground at a speed of 20 ms-1. Determine a) the time taken to reach 15 m above the groundb) velocity of the object at 15 m above the ground( Answer; a) t= 1.0 s or 3.0 s, b)for t= 1 s, v= -20 m…for t=3.0s, v= 10 mc) v= 20 ms-1 directed upwards, v= -10 ms-1 downwards)

2.2 Projectile motion

1. An object is thrown upwards at a speed of 30 ms-1 at an angle of projection of 60 o . . Determinea) the time taken by the object to reach maximum heightb) the maximum height reachedc) the ranged) the time taken to reach a height of 30 me) the velocity of object at a height of 30 m. ( assume g= 10 ms-2)( Answer ; t= 2.6 s , b) H= 33.8 m c) Range= 77.9 m d) t= 1.73 s or 3.47 s e) i)for time t= 1.73 s, instantaneous velocity= 17.3 ms-1 direction θ=30.1 withhorizontal , pointingupwardsii) for time t= 3.47 s, at the same height the speed is also 17.3 ms-1

θ=30.1 withhorizontal , pointingdownwards)

2. An airplane flies horizontally at a heght h in a straight line at a constant speed u. When it is directly a cannon on the grund, the cannon fires a sheel which is supposed to hit the airplane. Ignore air resistance. Determine in terms of u, g and ha) the minimum muzzle speed of the shellb) the angle of projection of the shell

3. An particle is shot from the horizontal ground at the roof of a horizontal 5.0 m high tunnel at a speed f 60 ms-1. Ignore air resistance. If the particle just barely touches the roof, determine the maximum range of the praticle( Assume g= 10 ms-2)( Answer; a) Height = 5.0 m, R=118 m)

4. A stone is shot from the ground at a speed of 100 ms-1 and at an angle of projection of 45o . Determine(a) the time of flight of the stone (b) the maximum height reached by the stone(c) the range of the stone( Answer; a) t= 14.1 s, b) H=250 m, c) R=500 m)

5. An object is thrown from the roof of a building of height 30.8 m at a speed of 23.8 ms-1 at an angle of projection 300. Determine the horizontal distance from the wall of the building to the point where the object strikes the ground( Assume g= 9.8 ms-2 )( Answer: Sx = 82.4 m )

6 An object on the roof of a building is thrown in a horizontal direction away from the building at a speed of 20 ms-1 .The time taken by the object to reach the ground is 2.0 s. Determine a) the velocity of the object 1.0 s after launching the objectb) the height of the buldingc) the horizontal distance from the base of the building travelled by the object when it reaches the ground( Answer ; a)angle= 26.60 with the horizontal b) Height = 20 m c) Sx = 40 m)

7. A person who stands 2.0 m away from a vertical wall throws a stone in a horizontal direction at a height of 1.6 m from the ground. Determine a) the time taken by the stone to reach the wallb) the initial speed of the stonec) the speed of the stone when it strikes the wall(Answer a) t= 0.28 s, b) Vx = 7.1 ms-1 c) angle= 21.50 with the horizontal)

Answer:Free fall under gravity without air resistance

Q1

Answer: Vertical motion upwards without air resistanceQ2

Answer projectile motionQ 1

Q 2

Q3