A package is dropped from a drone hovering at a height of 50 m above the ground. It falls freely under gravity for 2 s before a parachute opens. If the package must hit the ground with a safe impact speed of 10 m/s , the magnitude of the constant deceleration provided by the parachute is: (Take g = 10 m/s ^2 )

Step-by-step solution

During the first 2 s of free fall, the package starts from rest ( u = 0 ). Distance covered during free fall is h₁ = 1 2 gt^2 = 1 2 10 2^2 = 20 m . Velocity acquired after 2 s is v₁ = u + gt = 0 + 10 2 = 20 m/s . The remaining distance to the ground is h₂ = H - h₁ = 50 - 20 = 30 m . During this phase, the parachute provides a constant deceleration a . The initial velocity for this phase is 20 m/s and the final velocity is 10 m/s . Using the kinematic equation v_f^2 = v₁^2 + 2ah₂ : 10^2 = 20^2 + 2a(30) 100 = 400 + 6