Concept:
The second equation of motion can be defined as,
s = ut + (1/2) at²
where s is distance, t is time, u is initial velocity and a is the acceleration.
Given:
The velocity of projectile, V= (2î + 3j) m/s
Find:
The equation of trajectory.
Solution:
Given, V= (2i + 3j) m/s
The velocity in the i direction is 2i m/s.
The distance traveled in the i direction, that is in the x-axis, acceleration is zero in the x-axis,
s = ut + (1/2) at²
x = ut + (1/2) (0)t²
x = 2t m/s
The velocity in the j direction is 3j m/s.
The distance traveled in the j direction, that is in the y-axis, acceleration is 10m/s² in the downward y-axis,
s = ut + (1/2) at²
y = (3)t - (1/2) (10)t²
y = 3t - 5t²
So, writing x in terms of y,
y = (3/2)x - (5/4)x²
4y = 6x - 5x²
Hence, the equation of the trajectory is 4y = 6x - 5x² and the correct option is (b) 4y = 6x - 5x².
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