question 3 One of the contests at the school carnival is to throw a spear at an

Question

question 3

One of the contests at the school carnival is to throw a spear at an underwater target lying flat on the bottom of a pool. The water is 1.00m deep. You're standing on a small stool that places your eyes 2.90m above the bottom of the pool. As you look at the target, your gaze is 30? below horizontal. At what angle below horizontal should you throw the spear in order to hit the target?

a)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 trajectory.

Explanation / Answer

From snells law ,n sin tetha= sin ( pi /2 - alpha ) ------ sin tetha = cos alpha / n ------- tan tetha = cos alpha / (sqrt ( n^2 - cos alpha ^2 ))

From small triangle in water tan tetha = x / d

combining x = d tan tetha = d cos alpha / ( sqrt ( n^2 - cos alpha ^2))

From large triangle tan beta = ( h+d) / x + (h / tan tetha)

substituing for x ; tan beta = h +d / ( ( d cos alpha / (sqrt ( n^2 - cos alpha^2)) + h / tan alpha

we know d = 1 m , alpha = 30 degrees , h = 2.90m , n = 1.33

tan beta = 0.6627

beta = tan ^-1 ( 0.6627)

beta = 33.53 0

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

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