Physics - Velocity Question?

Question

A rock is thrown straight upward with an initial velocity of 9.6 m/s in a location where the acceleration due to gravity has a magnitude of 9.81 m/s^2. To what height does it rise?

I need the calculation(s) (based on what's avalable in the question) that is used to find the highest position the rock will have before it stops and begins to fall.

Answer 1

You don't need the distraction of "joules of energy." ### The simple kinematical formula is:

v^2 = 2 g h, ### so that h = (v^2) / (2 g) = (9.6)^2 / (2*9.81)

= 4.70 metres.

NOTE: Since the INITIAL INFORMATION is only given to 3 significant figures, the ANSWER should not be given to more than 3 significant figures. That's the way it is.

Live long and prosper.


### Note also: Should anyone object to what I'm saying, for example by claiming that "Well, you're USING the Principle of the Conservation of Energy," then they've forgotten how that principle arose, historically.

The kinematical equation "v^2 = 2 g h" first came about in Galileo's studies of gravitational acceleration, before the concept of energy and its conservation existed. He was doing experiments on the rolling and falling of balls and cylinders, etc.

Long before, monks in England had actually made ingenious timing measurements on falling bodies, so that the fact that distance fallen was proportional to (time squared) was already appreciated, experimentally However, Galileo was also interested in ALL the various relationships between things like any combination of v, t, distance, acceleration ... . From (strong!) hints provided by his experiments, he mathematically derived and then tested these various results.

Thus, the Principle of the Conservation of Energy, as essentially propounded by Galileo himself, FIRST AROSE through him interpreting the consequences of his established kinematical equation.

Answer 2

(final velocity)^2 = (initial velocity)^2 + 2(acceleration)(height)

The final velocity is 0 m/s since the rock stops at the height it reaches, and begins to descend downward.

0^2 = (9.6)^2 + 2(-9.81)h
-92.16 = -19.62h
h=4.697 m

I'm pretty sure that's right.

Answer 3

You initially give the rock kinetic energy of 0.5*m*v^2, or 46.08m joules of energy. At its highest point all the kinetic energy is converted to potential energy equal to m*g*h. Therefore...

46.08m=9.81*m*h
46.08=9.81*h
h=4.697 meters

Answer 4

So i'll in easy terms show you how to already know the technique to fixing it : First you're able to calculate the whole displacement travelled, with the help of multiplying the cost to time then you could sum up the whole time (upload mutually) finally, v = s/t = displacement / time So divide the whole displacement you purchased with the whole time you purchased this is properly-known speed P.S. do no longer forget approximately that speed is a vector, so make confident to offer the guidelines ! (East)