Answer: 16.8 m
Explanation:
The motion of the lemming is a projectile motion, consisting of two independent motions:
- on the horizontal (x) axis, a uniform motion, with constant speed v = 2.87 m/s
- on the vertical (y) axis, an accelerated motion, with constant acceleration [tex]g=-9.81 m/s^2[/tex] (downward)
The lemming lands in the water at x = 5.32 m away from the bas of the cliff, so we can calculate the time it takes to hit the water:
[tex]t=\frac{x}{v}=\frac{5.32 m}{2.87 m/s}=1.85 s[/tex]
And now, by considering the motion on the vertical direction:
[tex]y(t) = h +\frac{1}{2}gt^2[/tex]
we can find the height of the cliff (h) by requiring that y(t)=0:
[tex]0=h+\frac{1}{2}gt^2\\h=-\frac{1}{2}gt^2=-\frac{1}{2}(9.81 m/s^2)(1.85 s)^2=16.8 m[/tex]
