Question

Four balls A, B, C and D are projected with the same speed making angles of 20 deg, 30 deg, 45 deg and 80 deg with the horizontal. Which ball will strike the ground at nearest point?

Answer 1

`R(\theta_0=80^o)` is the minimum.

Explanation:

Range of the Projectile: `\qquad R= v_0^2/g\sin2\theta_0`

When the speed of projection `v_0` is the same, `R \propto \sin2\theta_0`

`\theta_0 = 20^o; \qquad \sin2\theta_0 = 0.6428;`
`\theta_0 = 30^o; \qquad \sin2\theta_0 = 0.8660;`
`\theta_0 = 45^o; \qquad \sin2\theta_0 = 1.0000;` Maximum
`\theta_0 = 80^o; \qquad \sin2\theta_0 = 0.3420;` Minimum

`R_{max} = R(\theta_0=45);`
Among the given angles the minimum range happens to be for a projection angle of `\theta_0=80^o`.