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[SOLVED] Lunar Gravity velocity on impact

karush

Well-known member
Jan 31, 2012
2,723
Lunar Gravity, On the moon, the acceleration due to gravity is $-1.6m/s$ . A stone dropped from a cliff on the moon and hits the surface of the moon $20s$ later.
How far did it fall?
What is the velocity at impact.?

well here I presume since the rock is just dropped that $v_0=1.6m/s$ but the time is known t=20s and

$f(t)=-1.6t^2+1.6t+S_0$

$f'(t)=-3.2t+1.6

but I don't think this is set up right.



Ans 320m; -32m/s
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Just a trivial matter perhaps, but the units of acceleration are distance per time squared.

Now, recall the kinematic equation for displacement given constant acceleration is:

$\displaystyle s(t)=\frac{1}{2}at^2+v_0t+s_0$

Since the rock is dropped, its initial velocity is zero. Its final height is zero, and it fell for 20 seconds. Hence, we may state:

$\displaystyle f(t)=-0.8t^2+s_0$

Solve for $\displaystyle s_0$ given:

$\displaystyle f(20)=0$

To find the velocity at impact, evaluate:

$\displaystyle f'(20)$
 

CaptainBlack

Well-known member
Jan 26, 2012
890
Lunar Gravity, On the moon, the acceleration due to gravity is $-1.6m/s$ . A stone dropped from a cliff on the moon and hits the surface of the moon $20s$ later.
How far did it fall?
What is the velocity at impact.?

well here I presume since the rock is just dropped that $v_0=1.6m/s$ but the time is known t=20s and

$f(t)=-1.6t^2+1.6t+S_0$

$f'(t)=-3.2t+1.6

but I don't think this is set up right.



Ans 320m; -32m/s
1. The units of the acceleration due to gravity are \(m/s^2\)

2. Dropped usually means that \(v_0=0\)

3. \( \displaystyle s(t)=\frac{g\; t^2}{2}+v_0 t +s_0 = - \frac{1.6\; t^2}{2}+s_0\)

When the rock hits the surface \(s(t)=0\), so ...

4. \(\displaystyle v(t)=g\;t+v_0 = \) ...

5. Since this is in calculus you need the supporting calculus: The equations in (3) and (4) above are obtained by integrating \(\ddot{s}= g\) and using \(v(t)=\dot{s}(t)\) with initial conditions \(\dot{s}(0)=v(0)=v_0\) and \(s(0)=s_0\).
 
Last edited:

karush

Well-known member
Jan 31, 2012
2,723
thanks much everyone, that was a great help:)


$0=-0.8(20)^2+S_o\ \ S_o=320m$

$f'(20)=-1.6(20) =-32m/s$


will be back with more, seem to slip and slide with this stuff.