Finding Initial Velocity Components of a Projectile Using Kinematic Equations

[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?

Homework Equations

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?

 

[voko]

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.

 

[Bashyboy]

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?

 

[voko]

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

 

[Bashyboy]

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

 

[voko]

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.