http://www.neonlightssigns.info/max-range/
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CP-06 AC/DC Current Probe (1mA to 40A range) Jaw Size max 6.5mm |  |
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Max Range
What angle of elevation gives the projectile max range? Justify your answer?
The range R of a projectile whose speed is v meters per second and whose angle of elevation is x radians is given by R=(v^2/g)sin(2x), where g=9.8 m/s/s is the acceleration due to gravity.
By the way this is hw for a college calc 1 class. Its not a graded thing. I just want to understand before class tonight hopefully. I figured that R'(x)= -cosx sinx and set it equal to zero to find extrema. But I came up with 0 and 90 degrees for nin and max which doesn't seem right. Can anyone shed some light on the sitch?
Forget the formula for a second and visualize the physics of it. The range an object travels is set by the curve the object follows leaving the ground and falling back down to it. If you aim too high (use a very high angle, like 85 degrees), the object will just go way up in the air and fall back down nearby. On the other hand, if you aim too low, like 0, which means horizontal, or negative angles, which means you're aiming at the ground, the object will not go very far.
The maximum distance it will go is when the angle is mid-way between vertical and horizontal, and the math will prove that.
The distance R(x) is k sin(2x). So, derivative of R is k 2cos(2x).
We know this by using d f(g(x))/dx = d f(x) d g(x) /dx.
So, d sin(2x) = cos(2x) d (2x) = cos(2x) 2 d(x) = 2cos(2x) dx.
To find the maximum value for sin(2x), set 2cos(2x) = 0 and check.
Cosine(x) crosses zero at pi/2 and -pi/2, but this is 2x, not x.
So, Cosine(2x) crosses zero at pi/4, 3pi/4, -pi/4 and -3pi/4.
The maximum occurs at x = pi/4 (45 degrees).
3pi/4 is the maximum in the opposite direction.
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CP-06 AC/DC Current Probe (1mA to 40A range) Jaw Size max 6.5mm | |
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US $65.99 | 10d 1h 25m |
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HONEYWELL MP953C 1026 2 SPRING RANGE 4-11 PSI MAX. SAFE | |
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US $29.99 | 29d 16h 27m |
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Dwyer 3005MR Photohelic Pressure Switch Gauge Range 0-5"W.C. Max.Pressure 25PSIG | |
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US $149.99 | 29d 13h 13m |
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AMETEK MODEL 88C001A2CS CAL RANGE 3/15 PSI MAX PRESS 15 PSI 104 KPA | |
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US $99.99 | 28d 19h 31m |
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MASTER PNEUMATIC PR-100-3 ADJ RANGE MAX INLET 300PSI | |
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US $20.00 | 28d 15h 52m |
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Jordan Valve Model 60-526 Max PSI 300 Range 30-95 1" | |
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US $175.00 | 25d 41m |
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NEW 1 1/2" CASH ACME VALVE REGULATOR TYPE B 250 PSI MAX SET 60 PSI RANGE 45-100 | |
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US $396.00 | 25d 32m |
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EXCELLENT USED ADJUSTABLE HOLLOW MILL 1 1/2 SHANK 1 INCH MAX RANGE CARBIDE BITS | |
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US $149.99 | 25d 15m |
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Star 601SPRD Star-Max Stock Pot Range, gas, one two-piece | |
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US $943.00 | 23d 21h 4m |
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New Johnson Controls P70DA-65 All-Range Pressure Control, SPST, 360PSIG Max | |
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Spring,Range,Induction,"Max",Countertop,208-220Volt,2600Watts,Cook&hold,#SM-261C | |
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Runescape High/Max Hits With Range (machinima)
if an object is projected horizontally 25m/s and 30. what is the max range, height, and horizontal direction?
if an object is projected horizontally 25m/s and 30. what is the max range, height, and horizontal direction?
i dont understand why it says that is projected horizontally 25m/s AND 30?
Please help!
The problem here is that '30' with no units attached is meaningless.
It obviously can't mean 30° because the word 'horizontally' was used just before it. If we assume it means the height above ground level, there is some hope:
Time to fall t = √(2y/g) = √(2*30/9.8) = 2.474 sec
Range R = Vh*t = 25*2.474 = 61.859 m
However asking for the height and horizontal direction is then a moot point......
If the 25 m/s IS actually at a 30° angle, the standard range eq → R = V²sin(2Θ)/g = 55.23 m
Hmax = V²sin²Θ/2g = 7.97 m.
This answer still doesn't address what is meant by 'find the horizontal direction'........
POORLY WORDED QUESTION!
