Projectile motion and acceleration HELP

[nrw]

Homework Statement

A lemming accelerates uniformly starting from rest 2 meters before jumping horizontally from the top of a 20 m high cliff. What is the minimum acceleration required so that the lemming can clear the rocks stretching out 4 m from the base of the cliff?

Homework Equations

I know that we have both an X and Y component we need to calculate, but what is confusing to me is that - how does the 2 meters at the beginning play into the horizontal velocity? And since the lemming is jumping horizontally - what does that mean? Does that mean something other than free fall? Is the initial velocity of the jump the final velocity of the horizontal velocity?

The Attempt at a Solution

I have tried this several ways, but have no idea if I'm doing it right. For the X component, I have the initial velocity is 0, the final velocity is unknown, the displacement is 2 m (??) and acceleration is 0 (because can acceleration exist in a horizontal dimension?) and the t is unknown. For the y component, I have the initial velocity as 0, but I don't know if this is correct? The acceleration is -10 m/s2, the Y displacement is -40. So, do I use the pythagorean theorem to find the final velocity of Y? I'm totally confused about where to start. Thanks!

 

[tiny-tim]

Welcome to PF!

Hi nrw! Welcome to PF!

Let's restate the problem more clearly …

i] a projectile leaves the top of a 20m cliff, with initial velocity purely horizontal, and lands 4m from the base: what is its initial speed, v₀?

ii] what acceleration must it have had to get from rest to v₀ after 2m?

 

[nrw]

Thanks! So when the initial velocity is purely horizontal, that means that we are assuming the initial speed of the fall is 0 and thus, the y-component is calculated using simple free fall acceleration?
I first calculated the time it would take the lemming to land if it were free falling... using y=Vi (t) - 1/2 a t2. This gives me 2 seconds. Then, if the lemming has only 2 seconds to clear 4 m, it must have a velocity of 2 m/s2 (using x=vt). Then, to calculate the acceleration, I use v2 = vi2 + 2aX and get the acceleration of 1 m/s.
Does that sound right?
I guess I'm confused about when to use a = -9.8 (all falls?) and when to break a equation up into both X and Y components.
Thanks!

 

[tiny-tim]

Thanks! So when the initial velocity is purely horizontal, that means that we are assuming the initial speed of the fall is 0 and thus, the y-component is calculated using simple free fall acceleration?

Yup!

I first calculated the time it would take the lemming to land if it were free falling... using y=Vi (t) - 1/2 a t2. This gives me 2 seconds. Then, if the lemming has only 2 seconds to clear 4 m, it must have a velocity of 2 m/s2 (using x=vt). Then, to calculate the acceleration, I use v2 = vi2 + 2aX and get the acceleration of 1 m/s.
Does that sound right?

Using g = 10, yes.

I guess I'm confused about when to use a = -9.8 (all falls?) and when to break a equation up into both X and Y components.

Don't ask yourself "what is the acceleration?" …

ask yourself "what is the force?"

If it's gravity, then it's 9.8 (or 10 ) …

if it's an applied force, then it isn't 9.8 !

(of course, sometimes it's both … eg a rocket)

But you must always break it up into X and Y components (or surface and normal, or whatever) …

F = ma is a vector equation, and you must treat it as such (unless of course the motion is obviously one-dimensional, in which case one of the component equations will be 0 = 0 )

 

[nrw]

Wow! Thank you so much for your help! Thinking of acceleration as force really helps - I appreciate your time and the way you ex;lain things!