Two projectiles, A and B, are shot at the same instant from the same location. P
ID: 1707795 • Letter: T
Question
Two projectiles, A and B, are shot at the same instant from the same location.Projectile A is shot at a speed of 560 m/s at and angle of 43 degrees (from horizontal)
and projectile B is shot at a speed of 680 m/s at an angle of 50 degrees. Determine
which projectile will hit the ground first. Then take the flying time, tf
, of that projectile and divide it into ten increments. At each time increment (from t=0 to t=tf), calculate the position vector rAB between the two projectiles. Display the results in a three-column matrix, where the columns are time and the x and y components of the position vector.
Explanation / Answer
projectile A==>vo=560 m/s==>vox=vo*cos()==>voy=vo*sin()
vox=560*cos(43º)409.56 m/s==>voy=560*sin(43º)381.92 m/s
total flight time=voy/g*277.943 s==>77.943/107.8 s each of 10 increments
projectile B==>vo=680 m/s==>vox=vo*cos()==>voy=vo*sin()
vox=680*cos(50º)437.1 m/s==>voy=680*sin(50º)520.91 m/s
total flight time=voy/g*2106.31 s==>106.31/1010.631 s each of 10 increments
Projectile A
time x-component y-component
in sec vox*t 1/2*g*t²+voy*t
7.8 3192.2 3277.1 from time 1 to time 9
15.6 6389.11 7150.4 time is 7.8 time 10 is closer
23.4 9583.66 11619.95 to actual time increment
31.2 12778.21 16685.73 not rounded like other 9
39 15972.76 22347.74
46.8 19167.32 28605.99
54.6 22361.87 35460.47
62.4 25556.42 42911.17
70.2 28750.98 50958.12
77.943 31922.18 59535.96 the 10 th increment
Projectile B
10.631 4646.76 6091.59
21.262 9293.53 13290.75
31.893 13940.29 21597.49
42.524 18587.05 31011.81
53.155 23233.82 41533.71
63.786 27880.58 53163.18
74.417 32527.34 65900.24
85.048 37174.1 79744.87
95.679 41820.87 94697.08
106.31 46467.63 110756.9 the 10 th increment
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