Mechanics and displacement questions

[Alserina]

Homework Statement

1) The Sun sets, fully disappearing over the horizon as you lie on the beach, your eyes 20 cm above the sand. You immediately jump up, your eyes now 170 cm above the sand, and you can again see the top of the Sun. If you count the number of seconds (t) until the Sun fully disappears again, you can estimate the radius of the Earth. Use the known radius of the Earth to calculate the time t.

Homework Equations

Earth's radius = 6375km

The Attempt at a Solution

I drew a picture of a circle (the earth) and the two tangent lines from h=20cm and h=170cm, but am not sure how to continue.

Homework Statement

2) Two students are asked to find the height of a particular building using a barometer. Instead of using the barometer as an altitude-measuring device, they take it to the roof of the building and drop it off, timing its fall. One student reports a fall time of 2.2s, and the other, 2.6s. What % difference does the 0.4s make for the estimates of the building's height?

Homework Equations

displacement = vt + 1/2at^2

The Attempt at a Solution

I can find the height of building for 2.2s and height of building for 2.6s but am not sure how to go about finding this % difference.

Homework Statement

2) Two students are asked to find the height of a particular building using a barometer. Instead of using the barometer as an altitude-measuring device, they take it to the roof of the building and drop it off, timing its fall. One student reports a fall time of 2.2s, and the other, 2.6s. What % difference does the 0.4s make for the estimates of the building's height?

Homework Equations

displacement = vt + 1/2at^2

The Attempt at a Solution

I can find the height of building for 2.2s and height of building for 2.6s but am not sure how to go about finding this % difference.

Homework Statement

A small source of light S is located at a distance L from a vertical wall. An opaque object with a height of h moves toward the wall with constant velocity v1 of magnitude v. At time t= 0, the object is located at the source S. Find an expression for vs, the magnitude of the velocity of the top of the object's shadow, at time t. Express the speed of the top of the object's shadow in terms of t, v, L, and h.

Homework Equations

The Attempt at a Solution

I drew a picture, but have no idea how to proceed after this.Any and all help is appreciated (:

 

[tiny-tim]

Welcome to PF!

Hi Alserina! Welcome to PF!

1) The Sun sets, fully disappearing over the horizon as you lie on the beach, your eyes 20 cm above the sand. You immediately jump up, your eyes now 170 cm above the sand, and you can again see the top of the Sun. If you count the number of seconds (t) until the Sun fully disappears again, you can estimate the radius of the Earth. Use the known radius of the Earth to calculate the time t.
…
I drew a picture of a circle (the earth) and the two tangent lines from h=20cm and h=170cm, but am not sure how to continue.

Hint: the Sun is infinitely far away in a fixed direction,

so the angle through which the Earth must have turned is … ?

2) Two students are asked to find the height of a particular building using a barometer. Instead of using the barometer as an altitude-measuring device, they take it to the roof of the building and drop it off, timing its fall. One student reports a fall time of 2.2s, and the other, 2.6s. What % difference does the 0.4s make for the estimates of the building's height?

Hint: you don't need to solve the equation, you only need to find what the equation is, and how it depends on t …

then just use "dimensions".

 

[ideasrule]

For the first question, see this thread:

https://www.physicsforums.com/showthread.php?t=332188

For the second, the question is asking how many percent of the answer the error takes up. If your error is 1 m and your calculated value is 10 m, for example, the percentage error would be 10%. If you have the heights calculated using the two data points, all you have to do is divide their difference by either the first height or the second.

Your third question would be easier if you find an expression for the position of the shadow's top in terms of t, v, L, and h. Then derive with respect to time and you'll get the requested equation.