Chapter 08, Problem 068 From the edge of a cliff, a 0.54 kg projectile is launch

Question

Chapter 08, Problem 068 From the edge of a cliff, a 0.54 kg projectile is launched with an initial kinetic energy of 1660 J. The projectile's maximum upward displacement from the launch point is +160 m. What are the (a) horizontal and (b) vertical components of its launch velocity? (c) At the instant the vertical component of its velocity is 77 m/s, what is its vertical displacement from the launch point? Take up to be the positive direction.

Chapter 08, Problem 068 From the edge of a cliff, a 0.54 kg projectile is launched with an initial kinetic energy of 1660 J. The projectile's maximum upward displacement from the launch point is -160 m. What are the (a) horizontal and (b) vertical components of its launch velocity? (c) At the instant the vertical component of its velocity is 77 m/s, what is its vertical displacement from the launch point? Take up to be the positive direction. (a) Number Units Units (b) Number (c) Number Units

Explanation / Answer

from the law of consevATION OF ENERGY

KEi + PEi = KEf + PEf

here PE i = 0

s0

1660 = 0.5 m * Vx^2 + mg (h)

1660 = 0.5 * 0.54 * Vx^2 + (0.54* 9.81* 160)

Vx = 54.85 m/s

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b. use KE = 0.5 mv^2 = 1660

0.5* 0.54 * V^2 = 1660

V = 78.41 m/s

as V^2 = Vx^2 + Vy^2

Vy^2 = V^2 - Vy^2

Vy^2 = 78.41^2 - 54.85^2

Vy = 56.03 m/s

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c. Use Vf^2 - Vi^2 = 2 a S

77^2 - 56.03^2 = 2 * 9.81* h

h = 142.18 m

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