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In a downhill ski race surprisingly little advantage is gained by getting a running start. This is because the initial kinetic energy is small compared with the gain in gravitational potential energy even on small hills. To demonstrate this, find the final speed and the time taken for a skier who skies 80.0 m along a 25° slope neglecting friction for the following two cases. (Note that this time difference can be very significant in competitive events so it is still worthwhile to get a running start.)(a) starting from restfinal speed  m/stime taken s(b) starting with an initial speed of 3.00 m/sfinal speed m/stime taken s

Question

In a downhill ski race surprisingly little advantage is gained by getting a running start. This is because the initial kinetic energy is small compared with the gain in gravitational potential energy even on small hills. To demonstrate this, find the final speed and the time taken for a skier who skies 80.0 m along a 25° slope neglecting friction for the following two cases. (Note that this time difference can be very significant in competitive events so it is still worthwhile to get a running start.)(a) starting from rest
final speed
  m/s
time taken
 s

(b) starting with an initial speed of 3.00 m/s
final speed
 m/s
time taken
 s

check_circleAnswer
Step 1

a)

The required final speed is,

1
mv=mglsin0
2
v 2(9.8)(30)sin (25)
=25.74 m/s
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Image Transcriptionclose

1 mv=mglsin0 2 v 2(9.8)(30)sin (25) =25.74 m/s

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Step 2

And the required taken time is,

gsine
25.74
(9.8)sin(25)
6.214 s
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Image Transcriptionclose

gsine 25.74 (9.8)sin(25) 6.214 s

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Step 3

b)

The required final...

1
1
mu=mglsin0
2
2
{03)(80)sin(25)}+(5)
=25.92 m/s
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Image Transcriptionclose

1 1 mu=mglsin0 2 2 {03)(80)sin(25)}+(5) =25.92 m/s

fullscreen

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