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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 3 / Problem 71P

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Solved: A 76.0-kg rock is rolling horizontally at the top

Chapter 3, Problem 71P

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QUESTION:

A 76.0-kg boulder is rolling horizontally at the top of a vertical cliff that is 20 m above the surface of a lake, as shown in Fig. P3.71. The top of the vertical face of a dam is located 100 m from the foot of the cliff, with the top of the dam level with the surface of the water in the lake. A level plain is 25 m below the top of the dam. (a) What must be the minimum speed of the rock just as it leaves the cliff so it will travel to the plain without striking the dam? (b) How far from the foot of the dam does the rock hit the plain?

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QUESTION:

A 76.0-kg boulder is rolling horizontally at the top of a vertical cliff that is 20 m above the surface of a lake, as shown in Fig. P3.71. The top of the vertical face of a dam is located 100 m from the foot of the cliff, with the top of the dam level with the surface of the water in the lake. A level plain is 25 m below the top of the dam. (a) What must be the minimum speed of the rock just as it leaves the cliff so it will travel to the plain without striking the dam? (b) How far from the foot of the dam does the rock hit the plain?

ANSWER:

Step 1 of 5

This problem can be considered as a projectile motion fired at an angle of $\ {0}^{0}$ from a height of “h”.

The total height is given as $20+25=45\ meters$ .

The horizontal distance is 100 meters.

So,

${x}_{0}=0$ and ${y}_{o}=h=45\ meters$ , which are the horizontal and vertical displacements of the ball.

Again,

$x={v}_{0}t$ --------------(1)

and $y=h-1/2\ g{t}^{2}$ -----------------(2)

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