Multiple choice

A person of height $2\ m$ wants to get a fruit which is on the top of a pole of height $\displaystyle \frac{10}{3}$ m if he stands at distance of $\left (\displaystyle \frac{4}{\sqrt{3}} \right ) m$ from the foot of the pole, then the angle at which he should throw the stone, so that it hits the fruit is .......... .

  1. $15^{\circ}$
  2. $30^{\circ}$
  3. $45^{\circ}$
  4. $60^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The person's eyes are at height 2m. The fruit is at height 10/3m. The vertical distance to clear is 10/3 - 2 = 4/3m. The horizontal distance is 4/sqrt(3)m. The tangent of the angle is (4/3) / (4/sqrt(3)) = sqrt(3)/3 = 1/sqrt(3). The angle whose tangent is 1/sqrt(3) is 30 degrees.

AI explanation

The effective height above the person's height is (10/3) minus 2, which equals 4/3 meters. Using the trigonometric ratio for tangent, we have tan(theta) = (4/3) divided by (4/sqrt(3)), which simplifies to 1/sqrt(3). The angle whose tangent is 1/sqrt(3) is 30 degrees, so he should throw the stone at an angle of 30 degrees.

Keep practicing — related questions