Question

Find a way to hang a painting on a wall with n nails, in such a way that the painting will fall if you take out either of the nails.

Answer #1

A painting is hung on a wall in such a way that its upper and
lower edges are 10 ft and 7 ft above the floor, respectively. How
far away from the wall should an observer whose eyes are 5 ft above
the floor stand in order to maximize the viewing angle? I need to
explain this topic ("The Best View") in a presentation and teach it
to a class.

A home run is hit in such a way that the baseball just clears a
wall 14 m high, located 132 m from home plate. The ball is hit at
an angle of 37° to the horizontal, and air resistance is
negligible. (Assume that the ball is hit at a height of 1.0 m above
the ground.)Find(a) the initial speed of the ball (b) the time it
takes to reach the wall and (c) the velocity components and the
speed...

A home run is hit in such a way that the baseball just clears a
wall 20 m high, located 128 m from home plate. The ball is hit at
an angle of 33° to the horizontal, and air resistance is
negligible. (Assume that the ball is hit at a height of 1.0 m above
the ground.)
(a) Find the initial speed of the ball.
m/s
(b) Find the time it takes the ball to reach the wall.
s
(c)...

Suppose that the options for 18-year-old students are (Go to
college, Fisherman, Hang out at their parents' place). Suppose you
estimate the Conditional Logit model to understand individual
preferences. Now, suppose that a 2 year ban on fishing makes the
choice to become a fisherman no longer feasible. The model implies
that you can still predict the ratio of the probability of going to
college over the probability of hanging out at their parents'
place. What would be this prediction?...

A person with weight 700 N stands d = 1.00 m away from
the wall on a ℓ = 9.00 m beam, as shown in this figure. The weight
of the beam is 5,000 N. Define upward as the positive y
direction and to the right as the positive x
direction.
(a) Find the tension in the wire. (Enter the magnitude only.)
N
(b) Find the horizontal component of the hinge force. (Indicate the
direction with the sign of your...

A 16.0-m uniform ladder weighing 490 N rests against a
frictionless wall. The ladder makes a 55.0° angle with the
horizontal.
(a) Find the horizontal and vertical forces the ground exerts on
the base of the ladder when an 820-N firefighter has climbed 4.20 m
along the ladder from the bottom.
Horizontal Force
magnitude
N
direction
---Select--- towards the wall away from the wall
Vertical Force
magnitude
N
direction
---Select--- up down
(b) If the ladder is just on the...

A 16.0-m uniform ladder weighing 490 N rests against a
frictionless wall. The ladder makes a 61.0° angle with the
horizontal.
(a) Find the horizontal and vertical forces the ground exerts on
the base of the ladder when an 820-N firefighter has climbed 4.30 m
along the ladder from the bottom.
Horizontal Force
magnitude
__N
direction
- towards the wall or away from the wall?
Vertical Force
magnitude
N
direction
up or down?
(b) If the ladder is just on...

In Bizarre Town the rules for the painting of buildings must to
be adhered to strictly. Each ﬂoor is to be painted one of black or
white and you can only paint a ﬂoor white if there is a black ﬂoor
immediately beneath it. Let pn be the number of legal ways to paint
a building with n ﬂoors. Find all legal paintings of buildings with
1, 2, 3 and 4 ﬂoors. Find a recurrence for the sequence
p1,p2,....

Find a recurrence relation for the number of ways to climb n
stairs if the person climbing the stairs can take 1, 2, or 3 stairs
at a time.
What are the initial conditions? Compute the number of ways to
climb 10 stairs in this way

A 86.8-kg climber is scaling the vertical wall of a mountain.
His safety rope is made of a material that, when stretched, behaves
like a spring with a spring constant of 1.76 x 103 N/m. He
accidentally slips and falls freely for 0.580 m before the rope
runs out of slack. How much is the rope stretched when it breaks
his fall and momentarily brings him to rest?

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