Question

A particle is to be projected so as to just graze each of the three identical rings of diameter 2 meter each, and placed in parallel vertical planes at a distances 4 meter apart with their highest points at a height 6 meter above the point of projection. Find the angle of projection ? Take g = 10 m/s^2

Answer 1

Question #79453, Physics / Mechanics | Relativity

A particle is to be projected so as to just graze each of the three identical rings of diameter 2 meter each, and placed in parallel vertical planes at a distance 4 meter apart with their highest points at a height 6 meter above the point of projection. Find the angle of projection? Take $g = 10 \, \text{m/s}^2$

Solution

The range of projection:

$$D = 8 \, \text{m}.$$

The maximum height:

$$H = 6 \, \text{m}.$$

The relation between the range R on the horizontal plane and the maximum height:

$$H = \frac{R}{4} \tan \theta$$ $$\tan \theta = \frac{4H}{R}$$ $$\theta = \tan^{-1} \frac{4H}{R} = \tan^{-1} \frac{4(6)}{8} = 72{}^\circ.$$

Answer: $72{}^\circ$.

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