Q. 48 Sam, whose mass is 75聽kg, strap... [FREE SOLUTION]

Chapter 10: Q. 48 (page 258)

Sam, whose mass is $75 k g$ , straps on his skis and starts down a $50$ -m-high, $20^{o}$ frictionless slope. A strong headwind exerts a horizontal force of $200$ N on him as he skies. Use work and energy to find Sam鈥檚 speed at the bottom.

Short Answer

Expert verified

Sam's speed at the bottom of the slope is $15.76 m / s .$

Step by step solution

Given information

Sam, whose mass is $75 k g$ straps on his skis and starts down a $50 m$ high, $20^{o}$ frictionless slope. A strong head wind exerts a horizontal force of $200 N$ on him as he skies.

Step 2:Explnation

Potential energy of a mass at height h is taken as mgh. KE of an object moving with velocity $v i s \frac{1}{2} m v^{2} .$

The component along the slope of the wind force acting on Sam is $200 \cos (胃) = 200 \cos (20^{o}) .$

Work done by the wind on Sam is

$W = F o r c e 脳 d i s \tan c e W = 200 \cos (20^{o}) 脳 h c s c (20^{o}) W = 200 c o t (20^{o}) 脳 50 W = 27, 474.77 J$

The KE of Sam at the bottom is

$\frac{1}{2} m v^{2} = m g h - W v^{2} = \frac{2 (m g h - W)}{m} v^{2} = \frac{2 (75 脳 9.81 脳 50 - 27, 474.77)}{75} v^{2} = 248.34 v = 15.76 m / s$

The other component (component perpendicular to the slope) of the wind force does no work as the friction between the skis and slope is zero.

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91影视

Sam, whose mass is $75 k g$ , straps on his skis and starts down a $50$ -m-high, $20^{o}$ frictionless slope. A strong headwind exerts a horizontal force of $200$ N on him as he skies. Use work and energy to find Sam鈥檚 speed at the bottom.

Short Answer

Step by step solution

Given information

Step 2:Explnation

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91影视

Sam, whose mass is 75kg, straps on his skis and starts down a 50-m-high, 20ofrictionless slope. A strong headwind exerts a horizontal force of 200N on him as he skies. Use work and energy to find Sam鈥檚 speed at the bottom.

Short Answer

Step by step solution

Given information

Step 2:Explnation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Energy Physics

Dynamics

Waves Physics

Modern Physics

Physics of Motion

Measurements

Study anywhere. Anytime. Across all devices.

Sam, whose mass is $75 k g$ , straps on his skis and starts down a $50$ -m-high, $20^{o}$ frictionless slope. A strong headwind exerts a horizontal force of $200$ N on him as he skies. Use work and energy to find Sam鈥檚 speed at the bottom.