Question

A 55 kg astronaut who weighs 180 N on a distant planet is pondering whether she can leap over a 7.0 m wide chasm without falling in. If she leaps at a 15-degree angle, what initial speed does she need to clear the chasm?

Answer 1

The initial speed need is 6.7689 m/s

Step-by-step explanation:

Given the data in the question;

first we determine the acceleration due to gravity in the distant planet;

g = F / m

given that; m = 55 kg and F = 180 N

g = 180 / 55

g = 3.2727 m/s²

Now, the relation between chasm distance and the initial speed;

d = v₀²sin2∅ / g

where d is the width of the chasm

we solve for v₀

v₀²sin2∅ = gd

v₀² = dg / sin2∅

v₀ = √[ gd / sin2∅ ]

so we substitute in our values;

v₀ = √[ (3.2727×7.0 ) / sin2(15°) ]

v₀ = √[ (22.9089 ) / sin( 15° + 15°) ]

v₀ = √[ (22.9089 ) / sin( 30°) ]

v₀ = √[ (22.9089 ) / 0.5 ]

v₀ = √[ 45.8178 ]

v₀ = 6.7689 m/s

Therefore, The initial speed need is 6.7689 m/s