The rogue river in oregon is so rocky in spots that jet boats have become a popular way for tourists to see wild stretches of the river. A system of air jets thrusting downward keep the boat suspended above the water and a second system of air jets move it horizontally. A jet boat driver comes around a bend in the river moving due west at a speed of 12 m/s when she discovers that a Douglas fir tree has fallen across the river 24 meters in front of her. She quickly reverses her horizontal jets so that they deliver a constant acceleration in an easterly direction.The jet boat slows down considerably and reaches the log after 4.0 seconds. What is its acceleration ? does it stop in time? Please show step by step

Expert Answers

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We assume the deceleration being constant over time (the motion from the initial speed `v_0 =12 m/s` until the boat reaches the log is uniform decelerated).

The equation that relates the space traveled to the initial speed, acceleration and time is

`s = v_0*t +(a*t^2)/2`

The data in text are `s = 24 m` and `t=4 s` . Therefore

`a = (s-v_0*t)*2/t^2 = (24-12*4)*2/4^2 = -3 m/s^2`

The speed of the boat when it reaches the log is

`v =v_0 +a*t =12 -3*4 =0 m/s`

This means that the boat stops exactly at the contact with the log (just in time).

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