You and your party of adventurers are being pursued by a pack of orcs. You know

Question

You and your party of adventurers are being pursued by a pack of orcs. You know that orcs aren’t particularly nimble, and so in an effort to get away you run to a nearby chasm with the intention to jump across. The chasm is 1.2 m wide and the ledge you are approaching is 30 cm lower than the one across the gap. You are running horizontally at a speed of 13 km/hr and you leap when you are 0.5 m from the edge of the chasm. You just barely make the jump, landing exactly at the opposite edge. What was your initial vertical velocity when you jumped? Assume that you did not change your horizontal velocity by jumping.

Explanation / Answer

Horizontal velocity =13 km/hr=3.61 m/s

Let us say vertical velocity is v m/s

Horizontal distance travelled=1.2+0.5=1.7 m

Time taken=1.7/3.61=0.47 sec

Vertical velocity=v

0.3=-v*0.47+4.9*0.47^2

We got v=1.66 m/s

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