For problems in which the object is projected vertically upward, you have to divide the problem into two parts. (1) Calculate the time to reach its maximum height and calculate the maximum height reached for the upward motion. (2) Reset the initial conditions to the position at maximum height where the initial velocity becomes and do the calculations for the downward movement of = 0 v0 the object. Velocity of the object negative and moving up Equation of motion Note: up is the positive direction valid only if The time tup to maximum height occurs when = 0 v The velocity as a function of time is v t The displacement as a function of velocity is x v The maximum height reached by the object occurs when = 0 xup v Example Small rock thrown vertically upward (v0 > 0) < 0 v0 = - u u = 0.010 kg = 1.0010-4 kg.m-1 = - 12.0 m.s-1 = 31.3 m.s-1 m v0 vT
For problems in which the object is projected vertically upward, you have to divide the problem into two parts. (1) Calculate the time to reach its maximum height and calculate the maximum height reached for the upward motion. (2) Reset the initial conditions to the position at maximum height where the initial velocity becomes v0 = 0 and do the calculations for the downward movement of the object. Velocity of the object negative and moving up Equation of motion Note: up is the positive direction valid only if The time tup to maximum height occurs when v = 0 The velocity v as a function of time t is The displacement x as a function of velocity v is The maximum height xup reached by the object occurs when v = 0 Example Small rock thrown vertically upward (v0 < 0 v0 = - u u > 0) m = 0.010 kg = 1.0010-4 kg.m-1 v0 = - 12.0 m.s-1 vT = 31.3 m.s-1