The airplane shown is in level flight at a height of 500m and a velocity of 42 m/s .If it were to release a heavy bomb, how much time would it take to hit the ground?
Answer (1)
1. Analyze the ProblemThe bomb's initial vertical velocity is 0 m/s (since the plane is in level flight).The bomb will fall under the influence of gravity (g ≈ 9.8 m/s²).We need to find the time it takes to fall 500 m.2. Choose the Appropriate Kinematic EquationWe can use the following kinematic equation for vertical motion:d = v₀t + (1/2)at²Where:d = vertical distance (500 m)v₀ = initial vertical velocity (0 m/s)a = acceleration due to gravity (9.8 m/s²)t = time (what we want to find)3. Substitute and Solve for Time (t)Substitute the known values into the equation:500 m = (0 m/s) * t + (1/2)(9.8 m/s²)(t²)Simplify and solve for t:500 m = 4.9 m/s² * t²t² = 500 m / 4.9 m/s²t² ≈ 102.04 s²t ≈ √(102.04 s²)t ≈ 10.1 sAnswer:It would take approximately [tex]\boxed{10.1}[/tex]seconds for the bomb to hit the ground.
