Kinematic equations: v_A = v_ + a_ delta t s_ = s_i + v_ delta t + 1/2 a_i (delt

Question

Kinematic equations: v_A = v_ + a_ delta t s_ = s_i + v_ delta t + 1/2 a_i (delta t)^2 v^2_A = v^2_ + 2a_ delta s The Rogue River in Oregon is so rocky in spots that jet boats 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 bent in the river moving due west at a speed of 12 m/s when she discovers that a large Douglas fir tree has fallen across the river 20 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 2.5 seconds. What is its acceleration? Does it stop in time? If not, how fast is it going when it hits the log? A) Draw a motion diagram and list all known values: B) Sketch the position, velocity and acceleration versus time graphs. C) Solution:

Explanation / Answer

S = ut + 1/2 at2

Here S = 20 m , u =12m/s, t =2.5 sec

20 = 12x 2.5 + 3.125a

1) a = -3.2 m/s2

let us see if it stops in time

V = u + at

= 12 -3.2 x 2.5

V= 4m/s

2) Since V is positive it doesnt stop in time

3) V = 4 m/s

Graphs

1) Distance Versus time graph :

This is a parabola with distance on the decreasing trend.

2) Velocity versus time graph

Thi is a straight line with accelaration as the slope m =3.2

3) Accelaration versus time

This is a constant horizontal line with Y intercept = 3.2

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