A 55- kg skier starts from rest at the top of a ski jump, point A in the figure

Question

A 55-kg skier starts from rest at the top of a ski jump, point A in the figure (Figure 1) , and travels down the ramp. Take that h= 40m.

Part A

If friction and air resistance can be neglected, determine her speed vBwhen she reaches the horizontal end of the ramp at B.

.

Express your answer to two significant figures and include the appropriate units.

Part B

Determine the distance s to where she strikes the ground at C.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

part A:

as friction and air resistance is neglected, energy conservation principle can be applied.

consider the motion from point A to point B.

initial total energy at point A=potential energy at A+kinetic energy at A

=mass*g*height+0.5*mass*speed^2

=55*9.8*40+0.5*55*0^2

=21560 J

final total energy at point B=potential energy at B+kinetic energy at B

=mass*g*height+0.5*mass*speed^2

=55*9.8*4.4+0.5*55*vB^2

=2371.6 + 27.5*vB^2

equating the two energy values:

21560=2371.6+27.5*vB^2

==>vB=26.415 m/s

part B:

consider the motion from B to C:

initial velocity at point B is 26.415 m/s , along horizontal direction.

let us consider x axis along the 30 degree incline and y axis along perpendicular to the incline.

then component of vB along x axis=vB*cos(30)=22.8761 m/s

component of vB along y axis=vB*sin(30)=13.2075 m/s

acceleration due to gravity along x axis=g*sin(30)=4.9 m/s^2

acceleration due to gravity along y axis=-g*cos(30)=-8.487 m/s^2

when the skier reaches point C, distance travelled along y axis =4.4/cos(30)=5.08068 m

as this distance travelled along -ve y axis, displacement=-5.08068 m

let time taken be t.

then using the formula:

displacement=initial velocity along y axis*time+0.5*acceleration along y axis*time^2

==>-5.08068=13.2075*t-0.5*8.487*t^2

==>t=3.45858 seconds

then distance travelled along x axis=initial velocity along x axis*time+0.5*acceleration along x axis*time^2

=22.8761*3.45858+0.5*4.9*3.45858^2=108.425 m

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