a man jumps from a balloon which is rising vertically at a constant rate of 2 mps at an elevation of 1415 m above the ground. The man waits 10 seconds before pulling the parachute cord. the parachute decelerates him at a uniform rate of 6 mps^2 until a speed of 6mps is attained. the man then descends to the ground at this constant speed. how long will it take him to reach the ground from the time he jumps from the balloon?

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\[\Delta y=h_o+v_ot-\frac12 gt^2\]\[v_1=v_0-gt\] at t=10, you will know the starting height and velocity of the next step\[\Delta y=h_1+v_1t-\frac12 gt^2\]determine the time by using the velocity information\[v=v_1-gt\]\[\frac{v-v_1}{-g}=t\]this will get you the time, and also allow you to calculate the height when the acceleration goes zero

the remaining distance covered at a constant speed is\[v=\frac{\Delta y}{\Delta t}\]\[\Delta t=\frac{\Delta y}{v}\]

sum up all the time intervals to get the total time elapsed :)

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