One of the contests at rthe school carnival is to throw a spear at an underwater

Question

One of the contests at rthe school carnival is to throw a spear at an underwater target lying flat on the bottom of a pool. The water is 1.10m deep. You're standing on a small stool that places your eyes 3.10m above the bottom of the pool. As you look at the target, your gaze is 30 degrees below horizontal. At what angle should you throw the spear in order to hit the target. Your raised arm brings the spear point to the level of your eyes as you throw it, and over this short distance you can assume that the spear travels in a straight line rather than a parabolic tragectory.

Explanation / Answer

Here ,

refractive index of watre , n2 = 1.33

for the water air interface ,

let the angle of refraction is r ,

angle of incidence , i = 90 - 30

i = 60 degree

Using snell's law

n1* sin(i) = n2 * sin(r)

1 * sin(60) = 1.33 * sin(r)

r = 40.6 degree

Now , horizontal distance of target ,

x = 3.1/tan(30) + 1.1 * tan(40.6)

x = 6.31 m

now , let the angle he shold throw is theta

theta = arctan((3.1 + 1.1 )/6.31)

theta = 33.65 degree

angle should you throw the spear in order to hit the target is 33.65 degree

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.