Question

a lemming runs from point A to a cliff at 4m/s, jumps over the edge at B and falls to C at average speed of 25 m/s. If the total distance from A to C is 500m and the time taken for the journey is 41 seconds, find the height BC of the cliff.​

Answer 1

Answer:

The height BC of the cliff is 400 m

Step-by-step explanation:

Let the distance between the point A to the cliff at B is x meters and the height BC is y meters.

So, x + y = 500 ....... (1)

⇒ 4x + 4y = 2000 .......... (2)

Now, at the speed of 4 m/s the time of travel from points A to B is $\frac{x}{4}$ sec. and at a rate of fall of 25 m/s the times taken to fall from B to C will be $\frac{y}{25}$ sec.

So, from the conditions given we can write  

$\frac{x}{4} + \frac{y}{25} = 41$ ....... (3)

⇒ 25x + 4y = 4100 ........ (4)

Now, solving equations (2) and (4) we get  

21x = 2100

⇒ x = 100 m

So,  from equation (1) we can write y = (500 - 100) = 400 m.

Therefore, the height BC of the cliff is 400 m (Answer)