# Reviewing Newtonian Mechanics

• Bashyboy
In summary, the problem involves a projectile being launched from ground level and reaching a displacement of 40 m horizontally and 53 m vertically. The horizontal component of the initial velocity can be determined, but the vertical component is unknown. Kinematic equations were attempted, but did not yield a solution. However, using a formula relating initial velocity, uniform acceleration, displacement, and time, the remaining unknown can be found. It is important to use the given data at a specific time, rather than setting time to 0.

#### Bashyboy

b]1. Homework Statement [/b]
1. Two seconds after being projected from ground level (y=0 m), a projectile is displaced
x=40 m horizontally and y=53 m vertically above its launch point. What are the (a) horizontal
and (b) vertical components of the initial velocity v of the projectile? (c) At the instant the
projectile achieves its maximum height above ground level, how far is it displaced horizontally
from the launch point?

## The Attempt at a Solution

I am working on part a). I was able to determine the horizontal component; however, I am unable to ascertain the vertical component of velocity. I tried applying kinematic equations, but with no avail. I tried to employ a symmetry argument, by finding the velocity acquired as the projectile falls to Earth from a vertical distance of 53 m, but then I realized that I don't know the velocity at this point, nor can I suppose that the speed is zero, because it isn't.

What should I do?

There is a formula relating initial velocity, uniform acceleration, displacement and time. You know three of these, thus should be able to find out the remaining unknown.

Are you speaking of this formula: vi = (y -.5at^2)/t. If so, how can I apply it when I need to set t = 0, in order to determine the initial velocity?

At what value of ##t## do you know ##y##? Why would you let ##t = 0## instead?

I figured that I would set t = 0, because that is the instant whose velocity I am trying to find.

At ## t = 0 ##, ## y = 0 ##, so your equation is ## 0 = v_i \cdot 0 - g \cdot 0^2 / 2 ##, which is useless. But you are given data at ## t ## different than 0, so use that.