In a scientific conducted in Arizona, a special cannon called HARP shot a projectile straight up to an altitide of 180.0km. If the projectile's initial speed was 3.00km/s, how long did it take the projectile to reach its maximum height?

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y=yo+vot+1/2gt^2

yo=0 assuming its on the ground

a=-g=9.8m/s^2

y=180km=180000m, 3.00km/s=3000m/s

Now

180000=3000t+1/2*(-9.8)t^2

or -4.9t^2+3000t-180000=0

using quadratic formula

t=-3000(+-)*squareroot(3000*3000-4*4.9*(-180000)/(2*-4.9)

Simplifying further

t=67.4s, and t=544s

Because we want to know how long it took to reach it originally we choose t=67.4s

Also 67.4 s and 544 s, the rocket is above 180 km and then falls back down to the 180 km point at the 544 s mark. so t=67.4s

Just a note on quadratic formula

Given ax^2 +bx+c=0

x can be found using the quadratic x=-b+-squareroot(b*b-4ac)/2a

Thank You!

Its my pleasure

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