Question

A Lemming is running 1.35m/s with its friends when it suddenly runs off a 34.6m tall cliff. How long was the lemming falling? How far did it land from the cliff?

Answer 1

The lemming was falling for approximately 2.65 seconds and it landed about 3.58 meters away from the base of the cliff.

Step-by-step explanation:

You have a two-part physics question regarding the motion of a lemming falling off a cliff. Let's solve each part using physics equations for motion under the influence of gravity.

Part 1: Time of Fall

The time taken by the lemming to fall can be calculated using the equation of motion for an object under free fall, which is h = 0.5 * g * t^2, where h is the height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time in seconds. Rearranging for t, we have t = sqrt((2 * h) / g).

Plugging in the height of the cliff (34.6 m), we get:

t = sqrt((2 * 34.6 m) / 9.8 m/s^2) ≈ sqrt(7.051 s^2) ≈ 2.65 seconds

Part 2: Distance from the Cliff

To find out how far the lemming landed from the base of the cliff, we use the horizontal velocity because the horizontal motion and vertical motion are independent of each other. The formula is distance = velocity * time.

Using the given horizontal velocity of the lemming (1.35 m/s) and the time of fall (2.65 s), we have:

distance = 1.35 m/s * 2.65 s ≈ 3.58 meters