Dock diving is a great form of athletic competition for dogs of all shapes and s

Question

Dock diving is a great form of athletic competition for dogs of all shapes and sizes. Sheba, the American Pit Bull Terrier, runs and jumps off the dock with an initial speed of 9.12 m/s at an angle of 23 degree with respect to the surface of the water. (Assume that the +x axis is in the direction of the run and the +y axis is up.) If Sheba begins at a height of 0.78 m above the surface of the water, through what horizontal distance does she travel before hitting the surface of the water?_____m Write an expression for the velocity of Sheba, in component form, the instant before she hits the water. (Express your answer in vector form.) v^rightarrow =_____m/s Determine the peak height above the water reached by Sheba during her jump.______m.

Explanation / Answer

v xi = vi cos theta = 9.12 m/s cos 23 = 8.39 m/s

vyi = vi sin theta = 9.12 m/s * sin 23 = 3.56 m/s

Apply kinematic equation

yf = yi + vyi t + 1/2 ay t^2

-0.78 m = 0+ ( 3.56 m/s) t + 1/2 ( -9.8) t^2

t^2( 4.9) - 3.56 t -0.78 m = 0

solving quadratic equation

t = 0.90 s

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vyf = vyi + ay t

vyf = 3.56 + (-9.8) ( 0.9) = -5.26 m/s

vf = sqrt vxf^2 + vyf^2 = sqrt ( 8.39)^2 + ( -5.26)^2 = 9.9 m/s

R = vf t = 9.9( 0.9) = 8.91 m

(b)

v = 8.39 m/s i + (-5.26 m/s) j

(c)

Hmax = vi^2 sin^2 theta/ 2g

= (9.12)^2 sin^2 ( 23)/ 2( 9.8)

=0.647 m

H' = H max + y = 0.647 + 0.78 = 1.427 m

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