Question

The skier starts from rest at $A$ and travels down the ramp. If friction and air resistance can be neglected, determine his speed $v_{B}$ when he reaches $B$. Also, compute the distance $s$ to where he strikes the ground at $C,$ if he makes the jump traveling horizontally at $B .$ Neglect the skier's size. He has a mass of $70 \mathrm{kg}$

Name: Problem 86, Chapter 14: Engineering Mechanics: Statics and Dynamics
Uploaded: 2020-12-22T01:57:24-08:00
Duration: 6 min 33 s
Channel: Rory Naguib
Description: The skier starts from rest at A and travels down the ramp. If friction and air resistance can be neglected, determine his speed vB when he reaches B. Also, compute the distance s to where he strikes the ground at C, if he makes the jump traveling horizontally at B . Neglect the skier's size. He has a mass of 70 kg

   The skier starts from rest at $A$ and travels down the ramp. If friction and air resistance can be neglected, determine his speed $v_{B}$ when he reaches $B$. Also, compute the distance $s$ to where he strikes the ground at $C,$ if he makes the jump traveling horizontally at $B .$ Neglect the skier's size. He has a mass of $70 \mathrm{kg}$

Engineering Mechanics: Statics and Dynamics

R. C. Hibbeler 14th Edition

Chapter 14, Problem 86

Instant Answer

Solved by Expert Rory Naguib

12/22/2020

Step 1

The total energy at point A (T_A) is the sum of kinetic and potential energy at A. Since the skier starts from rest, his kinetic energy is zero. His potential energy is given by mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. Show more…

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The skier starts from rest at $A$ and travels down the ramp. If friction and air resistance can be neglected, determine his speed $v_{B}$ when he reaches $B$. Also, compute the distance $s$ to where he strikes the ground at $C,$ if he makes the jump traveling horizontally at $B .$ Neglect the skier's size. He has a mass of $70 \mathrm{kg}$

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Key Concepts

Conservation of Energy

This principle states that in an isolated system, energy can neither be created nor destroyed, only transformed. In problems involving a skier or any object moving under gravity without friction, the loss of gravitational potential energy as the object descends is directly converted into kinetic energy. This conversion is used to calculate the speed of the object at different positions along its path.

Projectile Motion

Projectile motion describes the motion of an object that is launched into the air and moves under the effect of gravity alone. When an object leaves a surface with a horizontal velocity component, its motion can be split into constant horizontal motion and accelerated vertical motion. This concept allows us to calculate the time of flight and the horizontal distance traveled once the object loses contact with the surface.

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