A colony of lemmings, scared by a nearby hiker singing loudly out of tune, is ru

Question

A colony of lemmings, scared by a nearby hiker singing loudly out of tune, is running off a cliff with a horizontal launch speed of 1.38m/s. As a result, they will undergo a projectile motion. The cliff is 20m above a 10m-wide river and we neglect air drag.

(b) How far away from the base of the cliff will the lemmings land? As a side note, lemmings can swim the remaining distance to the shore.

(c) What is their flight time?

(d) Determine the velocity at landing by providing its magnitude and direction, and also write it in unit vector notation.

(e) A cat accidentally joined the lemmings in the flight but ran off the cliff at 29.8 Mph, also in the horizontal direction. Where does the cat land, what is her flight time, and velocity at landing?

Explanation / Answer

B) time of flight is T = sqrt(2h/g) = sqrt(2*20/9.81) = 2.01 S

Range R = u*T = 1.38*2.01 = 2.78 m

C) T = 2.01 S

D) v= sqrt(u^2 + (gt)^2) = sqrt(1.38^2 + (9.81*2.01)^2) = 19.76 m/s

direction is theta = atan(gt/u) = atan(9.81*2.01/1.38) = 86 degrees below the horizontal

in unit vector notation v = 1.38 i -19.71 j

e) 39.8 mph = 39.8*0.44704 = 17.8 m/s

Time of flight is T = sqrt(2h/g) = sqrt(2*20/9.81) = 2.01 S

R = u*T = 17.8*2.01 = 35.778 m

v = sqrt(17.8^2 +(9.81*2.01)^2) = 26.56 m/s

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