1 i think other people feel free to change this
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6.7
If h is vertical height, b=horizontal distance from wall to bottom of ladder and l=lenght of ladder,we can say lsquared = hsquared + b squared. Now differentiate w.r.t. time t. 2l*dl/dt= 2h* dh/dt + 2b*db/dt =0 However this solution doesn't give exactly the same answer when one solves the problem geometrically or using simple pythagorus. For example ,if l=20m and b=12 m and h=16m and db/dt is 2m/s, I calculate dh/dt as !.5 m/s using calculus but 1.717 m/s using geometry or straight Pythagorus. Where is the fallasy inthe method using calculus? Ray Bevan
To determine the maximum length a 95 kg person can climb up a 10 m ladder resting against a frictionless wall, we need to consider the forces acting on the ladder. The static friction force at the base of the ladder must be sufficient to counteract the moment created by the person's weight. Given the static friction coefficient of 0.40 with a total weight of the ladder and person, we can calculate the critical point where the ladder begins to slip. The maximum distance the person can climb before the ladder slips is approximately 4.19 m from the base, taking into account the ladder's angle and the distribution of forces.
Oh honey, we've got ourselves a classic right triangle situation here. Using some good ol' trigonometry, you can find that the angle between the ladder and the ground is approximately 83 degrees. Just remember, math may not be your friend, but it's definitely not your enemy either.
4
13 feet
If the wall is straight and the ground level then this is an outline of a right angle-triangle. If the top of the ladder makes an angle of 530 with the wall then the bottom of the ladder must make 370 to the ground. Use the sine ratio to find the length of the ladder (which will be the hypotenuse) sin = opp/hyp rearranged to hyp = opp/sin hyp = 15/sin370 = 24.92460212 feet So the length of the ladder is 25 feet correct to the nearest foot.
62+82=36+64=100 and the squared route of 100 is 10
6.7
If h is vertical height, b=horizontal distance from wall to bottom of ladder and l=lenght of ladder,we can say lsquared = hsquared + b squared. Now differentiate w.r.t. time t. 2l*dl/dt= 2h* dh/dt + 2b*db/dt =0 However this solution doesn't give exactly the same answer when one solves the problem geometrically or using simple pythagorus. For example ,if l=20m and b=12 m and h=16m and db/dt is 2m/s, I calculate dh/dt as !.5 m/s using calculus but 1.717 m/s using geometry or straight Pythagorus. Where is the fallasy inthe method using calculus? Ray Bevan
Yes, a ladder is a type of third-class lever, where the effort (force applied by the person climbing) is between the fulcrum (the point where the ladder rests on the ground) and the load (the weight of the person).
15*cos(60) = 7.5 7.5 m
Oh honey, we've got ourselves a classic right triangle situation here. Using some good ol' trigonometry, you can find that the angle between the ladder and the ground is approximately 83 degrees. Just remember, math may not be your friend, but it's definitely not your enemy either.
The bottom of an object is called the base.
The answer is foundation because it means the natural or prepared ground or base on which some structure rests.
The point of the elbow that rests on the table is generally called the olecranon process. It helps provide support when leaning on the table. Over time, prolonged pressure on the olecranon can cause discomfort or irritation, so it's important to adjust position to avoid strain.