Question

When an airplane leaves the runway, its angle of climb is 19° and its speed is 205 feet per second. How long will it take the plane to climb to an altitude of 10,000 feet? 16,000 feet?

Answer 1

well, the plane is climbing at 19 degrees angle
so say we'd like to know how long it'd take when it reaches 10,000 feet

so firstly... we may want to find how long horizontally has it travelled by the time it reaches 10,000 up

so now recall your SOH CAH TOA

so we're after the "adjacent side", but we only know the angle and opposite
thus we'd use the tangent identity

thus \(\bf tan(19^o)=\cfrac{opposite}{adjacent}\to \cfrac{y}{x}\implies tan(19^o)=\cfrac{10,000}{x}\implies x=\cfrac{10,000}{tan(19^o)}\)

Answer 2

hmm anyhow \(\bf tan(19^o)=\cfrac{opposite}{adjacent}\to \cfrac{y}{x}\implies tan(19^o)=\cfrac{10,000}{x}
\\ \quad \\
\implies x=\cfrac{10,000}{tan(19^o)}\)

Answer 3

So know solve for which is 29042?

Answer 4

solve for "x"*

Answer 5

we know is going 205 feet per second

so if we divide the horizontal by 205, should give us how many seconds it took to cover that horizontal distance

yeap

Answer 6

29042 yeap so 20942/205 thus 141.668 or 142 seconds

Answer 7

so to climb 10,000 feet UP it also travelled 29042 feet horizontally and it covered that in 142 seconds or 2mins and 22 secs

Answer 8

WOW!!

Answer 9

THANK-YOU

Answer 10

and to find how long for 16,000 just use that as the opposite side

Answer 11

yw

Answer 12

I didnt know what in the heck to do with the 205!