The horizontal range and maximum height attained by a projectile are R and H respectively. If a constant horizontal acceleration a = g ÷ 4 is imparted to the projectile due to wind in the direction of motion then its horizontal range and maximum height will be?
Answer should come (R + H), H
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Normal projectile motion , with no acceleration in horizontal direction.
H = u² sin² Ф / 2g u = initial speed, Ф angle of projection
R = u² sin 2Ф / g
With a constant acceleration due to wind in horizontal direction:
Time of flight remains same and is dependent on vertical component of velocity.
H" = same as H = u² sin² Ф / 2 g as there is no modification in y direction
R" = [u² sin 2Ф / g ] + 1/2 (g/4) (2 u sin Ф÷g)² , as acc = g÷4 t= 2 u sinФ÷g
= u² sin 2Ф / g + 1/2 u² sin² Ф / g
= R + H
H = u² sin² Ф / 2g u = initial speed, Ф angle of projection
R = u² sin 2Ф / g
With a constant acceleration due to wind in horizontal direction:
Time of flight remains same and is dependent on vertical component of velocity.
H" = same as H = u² sin² Ф / 2 g as there is no modification in y direction
R" = [u² sin 2Ф / g ] + 1/2 (g/4) (2 u sin Ф÷g)² , as acc = g÷4 t= 2 u sinФ÷g
= u² sin 2Ф / g + 1/2 u² sin² Ф / g
= R + H
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