A body is projected from the ground with some speed at some angle with the horizontal. Taking the horizontal and vertical direction to be x and y axes respectively and the point of projection as origin, calculate the minimum speed (in m s - 1 ) of projection so that it can pass through a point whose x and y coordinates are 30 m and 40 m respectively? Take g = 10 m s - 2

Step-by-step solution

In projectile motion, the equation of the trajectory is y = x tan ⁡ θ - g x 2 2 u 2 cos 2 ⁡ θ = x tan ⁡ θ - g x 2 2 u 2 1 + tan 2 ⁡ θ Substituting the given values, we have 40 = 30 tan ⁡ θ - 10 × 30 2 2 u 2 1 + tan 2 ⁡ θ or 900 tan 2 ⁡ θ - 6 u 2 tan ⁡ θ + 900 + 8 u 2 = 0 The value of tan ⁡ θ will be real if 6 u 2 2 ≥ 4 × 900 × 900 + 8 u 2 or u 4 ≥ 100 900 + 8 u 2 or u 4 - 800 u 2 ≥ 900