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
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).
Initial speed of the boat u= 12 m/s
acceleration a =?
distance cover = 24 m
time taken to cover 24 m = 4 sec
By the equation of linear motion
acceleration is negative ,it means retardation ,
Boat will stop.