Inverse square law and a particle being attracted because of it

Problem is on the attachment

gun fired an artiullary shell with speed v show that it can strike any target with in the surface given

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find the Lagrangian function

find the Lagrangian function on attachment. The bottom part of the attachment that got cut off just says "of motion of the particle.

Mechanics

The acceleration of a marble in a certain fluid is proportional to the speed of the marble squared and is given in SI units) by a=-3.00 v^2 for v greater than 0. If the marble enters this fluid with a speed of 1.20 m/s, how long will it take before the marble's speed is reduced to half of its initial value?

Speed of a ball

A ball is dropped from rest from a height h above the ground. Another ball is thrown vertically upwards from the ground at the instant the first ball is released. Determine the speed of the second ball if the two balls are to meet at a height of h/2 above the ground.

Velocity and Acceleration of a Pack

To protect his food from hungry bears, a boy scout raises his food pack with a rope that is thrown over a tree limb at height h above his hands. He walks away from the vertical rope with a constant velocity, vboy, holding the free end of the rope in his hands. a) Show that the speed v of the food pack is given by x(x^2+h^2)^(-1 ...continues

Vector Analysis

Having trouble working this problem

Vector notation

a) Vector E has a magnitude of 17.0 cm and is directed 27.0 degrees counterclockwise from the +x axis. Express it in unit vector notation. b) Vector F has a magnitude of 17.0 cm and is directed 27.0 degrees counterclockwise from the +y axis. Express it in unit vector notation. c) Vector G has a magnitude of 17.0 cm and is dire ...continues

Vector Components

In 1992, Akira Matsushima, from Japan, roe a unicycle across he United States, covering about 4800 km in six weeks. Suppos that , druing that trip, he had to find his way through a city with plenty of on way streets. In the city center, Matsushima had to travel in sequence 280 m north, 220 m east, 360 m north, 300 m west, 120 ...continues

position equation

The position of a particle which moves along a straight line is defined by: x=t^3-6t^2-15t+40, where x is in feet and t is in seconds. Determine the time at which the velocity will be zero, the position and distance traveled at that time, and the acceleration of the particle at that time.