Projectile Motion Problems 2
1. A paper ball on a table is flicked upwards at an angle of 180 from the horizontal with an initial speed of 2.1m/s
and lands on the table. Neglect air resistance.
a) What is the maximum height above the surface of the table?
b) What is the time of flight?
c) What is the range?
2. A cricket player bowls a ball on flat ground. The ball leaves his hand 2m above the ground at a speed of
100km/hr at an angle of inclination of 20. Neglect air resistance.
a) What is the time of flight?
b) What is the range?
c) What is the velocity of the ball when it hits the ground?
3. A hunter fires a gun on flat ground. The bullet leaves the gun at a speed of 210m/s at an angle of 140. The end of
the barrel is 25cm above the ground. Neglect air resistance.
a) What is the maximum height of the ball above the launch point?
b) What is the maximum height of the bullet above the ground? (Add 25cm to part a answer)
c) What is the time of flight?
d) What is the range?
e) What is the velocity of the bullet when it hits the ground?
4. An egg rolls off a 1.2m high kitchen bench and hits the ground. It is travelling at a speed of 0.4m/s when it
leaves the bench. Neglect air resistance.
a) What is the time of flight?
b) What is the range?
c) What is the velocity of the egg when it hits the ground?
5. An Aussie Rules player standing on a beach kicks a ball that lands on top of 10m cliff. The ball is kicked upwards
at an angle of 600 from the horizontal with an initial speed of 16m/s and leaves the players boot at a height of
1m above the beach. Neglect air resistance.
a) What is the maximum height of the ball above the launch point?
b) What is the maximum height of the ball above the beach? (Add 1m to part a answer)
c) What is the maximum height of the ball above the top of the cliff? (Subtract 10m from part b answer)
d) What is the time of flight?
e) What is the range?
6. A volley ball rolls off the roof of a 10m high school building with a roof sloped at 250 and hits the ground. It is
travelling at a speed of 0.5m/s when it leaves the roof of the building. Neglect air resistance.
a) What is the time of flight?
b) What is the range?
c) What is the velocity of the ball when it hits the ground?
7. A badminton player hits a shuttlecock at a speed of 4.3m/s at an angle of 800 from the horizontal. The
shuttlecock leaves the racket 1.2m above the ground. It clears a 2m net. Neglect air resistance.
a) What is the maximum height of the shuttlecock above the launch point?
b) What is the maximum height of the shuttlecock above the ground? (Add 1.2m to part a answer)
c) What is the maximum height of the shuttlecock above the top of the net? (Subtract 2m from part b answer)
d) What is the time of flight?
e) What is the range?
θ
Δy
u
ay
ux
uy
18
9.
8
1.997
219
0.648
936
2
9.
8
27.76
086
0.969
43
14
9.
8
203.7
621
50.80
36
0
9.
8
launc
h
Q
1
Q
2
Q
3
Q
4
Q
5
Q
6
Q
7
0
2.1
-2
27.77
778
0.2
5
1.2
+9
-10
1.2
210
0.4
16
0.5
4.3
0.4
0
60
9.
8
8
13.85
641
-25
9.
8
0.453
154
0.211
31
80
9.
8
0.746
687
4.234
673
Δymax from
launch point
vx
landing
vy
landing
t
Δx
v
θ
landing
landing
0.021485588
1.9972
1868
0.6489
357
0.13243
5855
0.264
503
2.1
-18
0.047948746
27.760
8563
6.3355
975
0.74541
1015
20.69
325
28.47
464
12.85
59
131.683958
203.76
2103
50.851
8
10.3729
9982
2113.
624
210.0
117
14.01
28
0.4
4.8497
423
0.49487
1659
0.197
949
4.866
21
85.28
5
9.795918367
8
3.9496
835
1.81694
7958
14.53
558
8.921
883
26.27
6
0
0.4531
5389
14.001
595
1.40717
1987
0.637
665
14.00
893
88.14
63
0.914921341
0.7466
8716
6.4383
584
1.08908
4866
0.813
206
6.481
512
83.38
47
0
𝑢𝑥 = 𝑢. cos 𝜃𝑙𝑎𝑢𝑛𝑐ℎ
𝑢𝑦 = 𝑢. sin 𝜃𝑙𝑎𝑢𝑛𝑐ℎ
At top of flight: ∆𝑦𝑚𝑎𝑥 =
𝑣𝑦 2 −𝑢𝑦 2
2𝑎𝑦
=
02 −𝑢𝑦 2
2𝑎𝑦
(Vertical velocity is zero at top of flight)
Landing: 𝑣𝑦 = −√𝑢𝑦 2 + 2𝑎𝑦 ∆𝑦 OR 𝑣𝑦 = −𝑢𝑦 (For projectiles launched and landing at same height)
Time of flight: 𝑡 =
𝑣𝑦 −𝑢𝑦
𝑎𝑦
𝑣𝑥 = 𝑢𝑥 (Neglecting air resistance)
Range: ∆𝑥 = 𝑢𝑥 . 𝑡
𝑣𝑙𝑎𝑛𝑑𝑖𝑛𝑔 = √𝑣𝑥 2 + 𝑣𝑦 2 (Vector addition of horizontal and vertical components of velocity)
𝑣𝑦
𝜃𝑙𝑎𝑛𝑑𝑖𝑛𝑔 = tan−1 ( )
𝑣𝑥