A hill is 500 m high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of 125 m s - 1 over the hill. The cannon is located at a distance of 800 m from the foot of the hill and can be moved on the ground at a speed of 2 m s - 1 so that its distance from the hill can be adjusted. What is the shortest time (in seconds) in which a packet can reach on the ground across the hill? (Take

Step-by-step solution

Given, height of the hill (h) = 500 m u = 125 m/s To cross the hill, the vertical component of the velocity should be sufficient to cross such height. ∴ u y ≥ 2 gh ≥ 2 × 1 0 × 5 0 0 ≥ 1 0 0 m/s But u 2 = u x 2 + u y 2 ∴ Horizontal component of initial velocity u x = u 2 - u y 2 = 1 2 5 2 - 1 0 0 2 = 7 5 m / s Time taken to reach the top of the hill t = 2 h g = 2 × 5 0 0 1 0 = 1 0 s Time taken to reach the ground from the top of the hill t' = t = 10 s Horizontal distance