Spark image

Projectile data

Projectile motion for initial height = 0 m, g = 9.81 ms-2


Units: velocity ms-1, angle degrees, time seconds, range m, height m.


Formulae used to calculate these values:

Maximum height reached = u2sin2A/2g
Horizontal motion: Distance travelled = ucosA t
Vertical motion: h = usinAt gt2

Initial velocity u, angle of projection A, total time for the projectile path (that given in the table) = 2t, maximum height h

To make the problem a little simpler is assumed that the projectile is always launched from ground level.

The range is taken to be the distance travelled horizontally by the projectile back to ground level.

Velocity
(ms-1)
Angle
(o)
Time
(s)
Range
(m)
Height
(m)
  Velocity
(ms-1)
Angle
(o)
Time
(s)
Range
(m)
Height
(m)
10 0 0 0 0   40 0 0 0 0
10 10 0.35 3.49 0.15   40 10 1.42 55.78 2.46
10 20 0.70 6.55 0.6   40 20 2.79 104.84 9.54
10 30 1.02 8.83 1.27   40 30 4.08 141.25 20.39
10 40 1.31 10.04 2.11   40 40 5.24 160.62 33.7
10 45 1.44 10.19 2.55   40 45 5.77 163.10 40.77
10 50 1.56 10.04 2.99   40 50 6.25 160.62 33.69
10 60 1.77 8.83 3.82   40 60 7.06 141.25 61.16
10 70 1.92 6.55 4.50   40 70 7.66 104.84 72.01
10 80 2.01 3.49 4.94   40 80 8.03 55.78 79.09
10 90 2.04 0.0 5.10   40 90 8.15 0.0 81.55
                     
Velocity
(ms-1)
Angle
(o)
Time
(s)
Range
(m)
Height
(m)
  Velocity
(ms-1)
Angle
(o)
Time
(s)
Range
(m)
Height
(m)
20 0 0 0 0   50 0 0 0 0
20 10 0.71 13.95 0.61   50 10 1.77 87.16 3.84
20 20 1.39 26.21 2.38   50 20 3.49 163.81 14.91
20 30 2.04 35.31 5.10   50 30 5.10 220.70 31.86
20 40 2.62 40.16 8.42   50 40 6.55 250.97 52.65
20 45 2.88 40.77 10.19   40 45 7.21 254.84 63.71
20 50 3.12 40.16 11.96   50 50 7.81 250.97 74.77
20 60 3.53 35.31 15.29   50 60 8.83 220.70 95.57
20 70 3.83 26.21 18.00   50 70 9.58 163.81 112.52
20 80 4.02 13.95 19.77   50 80 10.04 87.16 123.58
20 90 4.08 0.00 20.39   50 90 10.19 0.00 127.42
                     
Velocity
(ms-1)
Angle
(o)
Time
(s)
Range
(m)
Height
(m)
  Velocity
(ms-1)
Angle
(o)
Time
(s)
Range
(m)
Height
(m)
30 0 0 0 0   60 0 0 0 0
30 10 1.06 31.38 1.38   60 10 2.12 125.51 5.53
30 20 2.09 58.97 5.37   60 20 4.18 235.89 21.46
30 30 3.06 79.45 11.47   60 30 6.12 317.81 45.87
30 40 3.93 90.35 18.95   60 40 7.86 361.40 75.81
30 45 4.32 91.74 22.94   60 45 8.65 366.97 91.74
30 50 4.69 90.35 26.92   60 50 9.37 361.40 107.67
30 60 5.30 79.45 34.40   60 60 10.59 317.81 137.61
30 70 5.75 58.97 40.51   60 70 11.49 235.89 162.02
30 80 6.02 31.38 44.49   60 80 12.05 125.51 177.95
30 90 6.12 0.00 45.87   60 90 12.23 0.00 183.49

Further projection velocities follow.

Velocity
(ms-1)
Angle
(o)
Time
(s)
Range
(m)
Height
(m)
  Velocity
(ms-1)
Angle
(o)
Time
(s)
Range
(m)
Height
(m)
70 0 0 0 0   90 0 0 0 0
70 10 2.48 85.42 7.53   90 10 3.19 282.40 12.45
70 20 4.88 160.53 29.21   90 20 6.28 530.74 48.29
70 30 7.14 216.29 62.44   90 30 9.17 715.07 309.63
70 40 9.17 245.95 103.19   90 40 11.79 813.14 170.58
70 45 10.09 499.49 124.87   90 45 12.97 825.69 206.42
70 50 10.93 245.95 146.56   90 50 14.06 813.14 242.27
70 60 12.36 216.29 187.31   90 60 15.89 715.07 309.63
70 70 13.41 160.53 220.53   90 70 17.24 530.74 364.55
70 80 14.05 85.42 242.21   90 80 18.07 282.40 400.40
70 90 14.27 0.00 249.75   90 90 18.35 0.00 412.84
                     
Velocity
(ms-1)
Angle
(o)
Time
(s)
Range
(m)
Height
(m)
  Velocity
(ms-1)
Angle
(o)
Time
(s)
Range
(m)
Height
(m)
80 0 0 0 0   100 0 0 0 0
80 10 2.83 223.13 9.84   100 10 3.54 348.64 15.37
80 20 5.58 419.35 38.16   100 20 6.97 655.24 59.62
80 30 8.15 564.99 81.55   100 30 10.19 882.80 127.42
80 40 10.48 642.48 134.78   100 40 13.10 1003.9 210.59
80 45 11.53 652.40 163.10   100 45 1019.4 509.68 254.84
80 50 12.49 642.48 191.42   100 50 15.62 1003.9 299.09
80 60 14.12 564.99 244.65   100 60 17.66 882.80 382.26
80 70 15.33 419.35 288.04   100 70 19.16 655.24 450.06
80 80 16.07 223.13 316.36   100 80 20.09 348.8 494.32
80 90 16.31 0.00 326.20   100 90 20.39 0.00 509.68
 

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© Keith Gibbs 2020