Suppose we climb a mountain that is a cone with radius ro= 100 and height h = 4. We start at the bottom of the mountain (on the perimeter of the base of the cone), and our destination is the opposite side of the mountain, halfway up (height h= 2). Our climbing speed starts at V0 = 2 but gets slower at a rate inversely proportional to the distance to the mountain top (so at height z the speed is (h-z)vo/h). Find the minimum time needed to get to the destination.

Suppose we climb a mountain that is a cone with radius ro= 100 and height h = 4. We start at the bottom of the mountain (on the perimeter of the base of the cone), and our destination is the opposite side of the mountain, halfway up (height h= 2). Our climbing speed starts at V0 = 2 but gets slower at a rate inversely proportional to the distance to the mountain top (so at height z the speed is (h-z)vo/h). Find the minimum time needed to get to the destination.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter4: Motion In Two And Three Dimensions

Section: Chapter Questions

Problem 56P: Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a...

See similar textbooks

Similar questions

If the magnitude of the acceleration due to gravity on Earth's surface is 9.8 m/s2, what is the magnitude of the acceleration due to gravity at an altitude equal to Earth's radius?
An ice skater is executing a figure-eight, consisting of two identically shaped, tangent circular paths. Throughout the first loop, she increases her speed uniformly, and during the second loop she moves at a constant speed. When the ice skater travels during the first loop, the acceleration vector is not directed towards the center, whereas when the ice skater travels in the second loop, the acceleration vector is directed toward the center. Is this true or false?
A proton has a speed 5x106m/s and is moving in a circle in the xy plane of a radius r = 0.175m.what is its position in the xy plane at time t= 2.0x10-7 s? at t= 0, the position of the proton is 0.175mî and its circles counter clockwise.sketch the trajectory.
The radius of the earth is R. At what distance above the earth's surface, in terms of R , is the acceleration due to gravity = 2.5 m/s2 ? At approximately (answer) × R above the earth’s surface.
An experimental jet rocket travels around Earth along its equator just above its surface. At what speed must the jet travel if the magnitude of its acceleration is g?
An object moving at constant speed v around a circle of radius r has an acceleration a directed toward the center of the circle. The SI unit of acceleration is m/s2. If the speed is increased 17.5%, by what percentage does the radial acceleration increase?
A distant planet has a mass of 5.00 x 1023 kg and a radius of 6.00 x 106 m. Someone is standing on the surface of the planet and throws a rock straight up with initial speed of 7.0 m/s. What is the maximum hight reached by the rock above the point from where it was thrown?
The earth has a radius of 6380 km and turns around once on its axis in 24h. a) What is the radial acceleration of an object on the ground at the earth’s equator? Give your answer in units of m/s and compare your result with the gravitational acceleration g. b) What is the radial acceleration of an object on the ground at the earth’s geographic North pole?
Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what initial velocity (in m/s) would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7 m/s2. (Assume the volcano is radially symmetric and the summit is at its center. Enter the magnitude.)
A runner taking part in the 200 m dash must run around the end of a track that has a circular arc with a radius of curvature of 35 m. If he completes the 200 m dash in 24.2 s and runs at constant speed throughout the race, what is the magnitude of his centripetal acceleration (in m/s2) as he runs the curved portion of the track?
For an object undergoing a uniform circular motion with radius 5.7 m and period 4.35 sec, the centripetal acceleration (m/s2) is:
If the speed of an object in uniform circular motion is tripled and the radial distance remains constant, then the magnitude of the centripital acceleration increases by what factor?