Projectile motion and kinetic energy

[cheybe3]

Homework Statement

A .550 kg projectile is launched from the edge of a cliff with an initial kinetic energy of 1550 J and at its highest point is 140 m above the launch point.

a. What is the horizontal component of its velocity?

b. What was the vertical component of its velocity just after launch?

c. At one instant during its flight the vertical component of its velocity is found to be 65.0 m/s. At that time, how far is it above or below the launch point?

Homework Equations

K=1/2mv^2

projectile motion equations

The Attempt at a Solution

I used the kinetic energy equation to find an initial velocity of about 75 m/s. but now I'm not sure how to proceed...I feel like there are too many unknowns. My first approach was to try and figure out the measure of the angle of projection using various projectile motion equations knowing that the vertical component of velocity at it's highest point is zero, and that the y position is 140 m. but i kept coming up w/too many unknowns...i'm stumped! any help would be greatly appreciated.

 

[tiny-tim]

Welcome to PF!

Hi cheybe3 ! Welcome to PF!

I used the kinetic energy equation to find an initial velocity of about 75 m/s. but now I'm not sure how to proceed..

Call the angle θ, and the time to get to the highest point t, and write out equations for the x and y components (separately): that should enbable you to elminate t and to find θ.

Show us how far you get. ​

 

[cheybe3]

but i don't know x so wouldn't the equation for the x component then contain 3 unknowns...the x component, the angle theta, and the time?

 

[tiny-tim]

oops! i misread the question …

you don't need an x equation at all …

just use the y component of velocity, and find what it has to be if the highest point is 140m.

 

[vela]

Think about the projectile's velocity at the top of its trajectory and finding its kinetic energy at that point.

 

[cheybe3]

the only equations we've gone over for deriving the x/y components of velocity require us to know the measure of angle theta, or the time...i still seem to be having trouble with too many unknowns.

 

[ehild]

Just think of energy conservation. What is the potential energy at the top of trajectory with respect to the launch point? What is the kinetic energy there? What is the direction of the velocity at the top of the trajectory?

ehild