An archaeologist is trying to measure the height of a small window in an old tower....

An archaeologist is trying to measure the height of a small window in an old tower. He brought
an instrument that allows him to measure angles with great precision and accuracy, but arithmetic
is not one of his strengths and he unforunately forgot to bring a calculator. He can, however, do
simple additions and multiplications. To measure the window, he stands at a distance of 120 m
from the base of the tower from where he sees the bottom of the window frame under an angle of
Pi/4 rad and the top of the frame under an angle of pi/4+0.005 rad. He remembers what he
learned from his youth and manages to compute the height of the window to
an accuracy of 1 cm. If an archaeolgist can do this, then so can you. Compute the height of the
window by using the quadratic Taylor polynomial of tan theta around theta=Pi/4.

Expert Solution

genius_generous answered 2 years ago

If the tower is 45 feet in height, how far is the partner from the base of the tower?

From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of depression of 40 degrees. If the tower is 45 feet in height, how far is the partner from the base of the tower?

A tower worker at the top of a wind turbine tower is letting down a small...

A tower worker at the top of a wind turbine tower is letting down a small broken part of mass 4.3 kg tied to a practically massless rope. The top of the tower is 14.4m above the ground, and the wind is blowing at 6.3 m/s at the top of the tower and decreases linearly with height to 1.7 m/s at the ground. She is letting the rope slide thru her leather gloves at a rate of 0.30 m/s, and...

Suppose that a cannon tower of 1000 feet height was erected at the origin of the...

Suppose that a cannon tower of 1000 feet height was erected at the origin of the coordinate space. The speed of the cannonballs launched by the tower is 1000 feet per second. An armored vehicle is patrolling in a circular path around the tower 8000 feet away at a speed of 10 feet per second. Coordinates was chosen such that at time zero the location of the vehicle is (8000, 0, 0). (a) Describe the motion of the vehicle with...

A rock is thrown at a window that is located at a height h = 36.33...

A rock is thrown at a window that is located at a height h = 36.33 m above the ground. The rock is thrown at an angle of θ above horizontal. The rock is thrown at time 0 seconds from a height of hi = 2.00 m above the ground with an initial speed of v0 and experiences no appreciable air resistance. After t = 2.0 seconds, let the velocity of the rock be v =(15.00 i + 6.38 j...

From the window of a building, a ball is tossed from a height y0 above the...

From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 7.90 m/s and angle of 19.0° below the horizontal. It strikes the ground 6.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical...

WUC Window, Inc., is trying to determine the cost of its debts.

Calculating Cost of Debt: WUC Window, Inc., is trying to determine the cost of its debts. The firm has a debt issue outstanding with seven years to maturity that is quoted at 108 percent of face value. The issue makes semiannual payments and has embedded cost of 6.1 annually. a) What is a WUC"s pretax cost of debt? b) If the tax rate is 38 percent, what is the after-tax cost of debt?

1. The Eiffel Tower is a steel structure whose height increases by 19.8 cm when the...

1. The Eiffel Tower is a steel structure whose height increases by 19.8 cm when the temperature changes from -9 to +40 oC. What is the approximate height (in meters) at the lower temperature? 2. Many hot-water heating systems have a reservoir tank connected directly to the pipeline, so as to allow for expansion when the water becomes hot. The heating system of a house has 87.3 m of copper pipe whose inside radius is 9.70 x 10- 3 m....

heat transfer The double-glazed window with a height of 1.2m and a width of 2m has...

heat transfer The double-glazed window with a height of 1.2m and a width of 2m has a gap of stagnant air (k = 0.026W / m ° C) with a width of 12mm between the glass of 3mm (k = 0.78W / m ° C). On a day when the outside temperature is kept at 24 ° C, find the continuous heat transfer rate and inner surface temperature in this glass window. (Take the heat transfer coefficients h1 = 10W...

1. A stone is thrown upward from a tower with initial velocity of 3 m/s. Height...

1. A stone is thrown upward from a tower with initial velocity of 3 m/s. Height of tower is 50 m above the ground. What would be its position after 3.4 secs? What would be its speed after 3.4 secs? What would its velocity be when it hits the ground? 2. Duterte throws a ball upward at 15 m/s while standing on the edge of a building so that the ball can fall to the base of the building 50...

A ball is tossed vertically upward from a window, height 50.0 m above the ground. The...

A ball is tossed vertically upward from a window, height 50.0 m above the ground. The initial speed of the ball is 25.0 m/s. The ball goes up and comes down, landing on the ground at the base of the building. Determine the following: a) The time it took the ball to reach its maximum height above ground. b) The maximum height above the ground. c) The time the ball returns to its initial height. d) The velocity of the...

Question