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A particle is projected with a velocity of A 20m/s in air at an angle alpha with horizontal. The x and y coordinates lying on trajectory of the particle with respect to point of projection R, 20m and 8m respectively. Find the angle of projection of the particle.

A particle is projected with a velocity of A 20m/s in air at an angle alpha with horizontal. The x and y coordinates lying on trajectory of the particle with respect to point of projection R, 20m and 8m respectively. Find the angle of projection of the particle.

Grade:12th pass

1 Answers

Shivam Agrawal
14 Points
4 years ago
Let the point of projection have the coordinates (0,0). Then the coordinates after ‘t’ time is [20*t*cos(alpha), 20*t*sin(alpha)].
Coordinates given (20,8) 
Therefore, 
20*t*cos(alpha) = 20
t*cos(aplha) = 1    -------------- (1)
 
20*t*sin(alpha) = 8
t*sin(alpha) = 2/5    ---------------(2)
 
Dividing equation (2) by (1)
 
[t*sin(alpha)] / [t*cos(alpha)] = 2/5
tan(alpha) = 2/5
alpha = tan-1(2/5) 
Angle of Projection = tan-1(2/5)

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