What Is the Minimum Speed Needed for a Boulder to Clear the Dam?

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To determine the minimum speed needed for a 76 kg boulder to clear a dam while rolling off a 20 m cliff, calculations show that the time to fall is approximately 2.02 seconds. The horizontal distance to the dam is 100 m, leading to a required horizontal speed of about 45.45 m/s. However, a participant in the discussion suggests re-evaluating the arithmetic, indicating that the correct calculation may yield a slightly different value. The conversation highlights the importance of accurate calculations in physics problems. Ultimately, the focus remains on ensuring the boulder travels the necessary distance without striking the dam.
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Homework Statement



a 76 kg boulder is rolling horizontally at a top of a vertical cliff that is 20m above the surface of a lake. 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. what must the minimum speed of the rock be just as it leaves the cliff so that it will travel to the plain without striking the dam?

Homework Equations





The Attempt at a Solution



20= 4.9 * t^2
20/4.9= t^2
t=square 20/49
t=2.02

100 = vx0 * t
100/2.02 = vx0
vx0 = 45.45 m/s

20+25 = .5 * 9.8 * t^2
45 = 4.9* t^2
t+3.03

V0x * 3.3 = 150m
45.45*3.3 = 150
150-100 = 50m

I am not getting the min speed. Is it the 45.45? I believe so, but the program doesnt. Appreciate any help. The 50 m is correct.
 
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Bottomsouth said:
20= 4.9 * t^2
20/4.9= t^2
t=square 20/49
t=2.02

100 = vx0 * t
100/2.02 = vx0
vx0 = 45.45 m/s
Redo that last bit of arithmetic.
 
49.5, thanks. Have had very little sleep.
 

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