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Question

Standing side by side, you and a friend step off a bridge at different times and fall for 1.6 s into the water below. Your friend goes first, and you follow after she has dropped a distance of 2.0 m. 

a. When your friend hits the water, is the separation between the two of you 2.0 m, less than 2.0 m, or more than 2.0 m? Explain your reasoning. 

b. Verify your answer to part (a) with a calculation.

Answer 1

a. More than 2 m. First calculate the total distance from the point of the jump-off to the water. This is given by S = 1/2 g t². As the time required to reach the water is given as 1.6 s, the distance to the water is 12.54 m. The time for her to fall 2 m at which time you jump is t = √2m x 2/ 9.8 ms^-2 = 0.639 s. The friend will travel an additional (1.6 - 0.639) 0.961s before hitting the water during which time you will have fallen S = 1./2 g t² = 1/2 x9.8 x 0.961² = 4.53 m. As the height of the drop was 12.54 m and at the time your friend hit the water, you had fallen 4.53 m, the separation between you would be about 8 m.