Problemas
A girl jumps off a diving board that is 3m high. If she jumps of the board at 8m/s How high does she get in the air? square At what velocity does she hit the water? square
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Aitor
maestro · Tutor durante 5 años
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Respuesta
To solve this problem, we need to use the kinematic equations of motion under constant acceleration due to gravity.Given information:- The diving board is 3 m high.- The girl jumps off the board at a velocity of 8 m/s.Step 1: Calculate the maximum height the girl reaches in the air.We can use the kinematic equation:h = (v^2) / (2g)Where:h = maximum heightv = initial velocityg = acceleration due to gravity (approximately 9.8 m/s^2)Substituting the given values:h = (8 m/s)^2 / (2 × 9.8 m/s^2)h = 64 m^2/s^2 / 19.6 m/s^2h = 3.27 mTherefore, the girl reaches a maximum height of 3.27 m in the air.Step 2: Calculate the velocity at which the girl hits the water.We can use the kinematic equation:v_f^2 = v_i^2 + 2asWhere:v_f = final velocityv_i = initial velocitya = acceleration (due to gravity)s = displacement (downward distance)Since the girl starts from the diving board and falls 3 m, the displacement is -3 m (downward).Substituting the given values:v_f^2 = (8 m/s)^2 + 2 × (-9.8 m/s^2) × (-3 m)v_f^2 = 64 m^2/s^2 + 58.8 m^2/s^2v_f^2 = 122.8 m^2/s^2v_f = √(122.8 m^2/s^2)v_f = 11.08 m/sTherefore, the girl hits the water at a velocity of 11.08 m/s.