You have been stranded on a deserted island. Fortunately, you managed to bring a

Question

You have been stranded on a deserted island. Fortunately, you managed to bring a flare gun. You can see a ship 300 m off shore. Unfortunately, because of the daylight the ship cannot see your flare unless it is within 100 m of the ship. If you fire the flare gun from the shore line with an initial velocity of 161 km/hr at an angle of 33.3 degree, will they see your flare? (You must show your work in explaining why/why not.) With this same initial speed, is there an angle you could fire that would allow them to see your flare? If so, what is that angle?

Explanation / Answer

formula for range is

R = u cos theta ( 2 u sin theta/ g)

= u^2 / g * sin 2 theta

= ( 161( 5/18)^2 /9.8 * sin 2( 33.3)

= 187.30 m

the distance is not same as 200 m so you cannot see the flare

(b)

200 m = ( 161( 5/18)^2 /9.8 * sin 2( theta)

2 theta = 78.63

tehta = 39.31 degree

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