Given: u = 40 ms-1, t = 2 s, y = 20.4 m,
ay = -9.8 m/s2
To find:
(i) Angle of projection (θ)
(ii) Horizontal range of projectile (R)
Formulae: (i) y = uy t + \(\frac{1}{2}\) ay t2
(ii) R = \(\frac{u^2\,sin\,2\theta}{g}\)
Calculation: Taking vertical upward motion of the projectile from point of projection up to the top of vertical pole we have
uy = 40 sinθ,
From formula (i),
∴ 20.4 = 40 sinθ × 2 + \(\frac{1}{2}\) (-9.8) × 22
∴ 20.4 = 80 sinθ – 19.6
or sinθ = \(\frac{(20.4+19.6)}{80}=\frac{1}{2}\)
or θ = 30°.
From formula (ii),
Horizontal range = \(\frac{40^2}{9.8}\) sin 2 × 30°
= 141.4 m
The angle of projection is 30°. The horizontal range of projection is 141.4 m