A body is thrown at 30° to the horizontal at 15 m/s. Find the range — Physics problems | PhysLabo
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Range of a projectile thrown at 30°

Medium 9 grade Mechanics / Motion

A body is thrown at an angle $\alpha = 30°$ to the horizontal with speed $v_0 = 15$ m/s. Find the range of the body (the horizontal distance). The acceleration due to gravity is $g = 10$ m/s²; neglect air resistance.

Given
  • $v_0 = 15$ m/s
  • $\alpha = 30°$
  • $g = 10$ m/s²
  • $L = ?$
Hints
Hint 1 / 2
Use the range formula with $\sin 2\alpha$: double the angle before substituting.
Hint 2 / 2
$\sin 60° = \sqrt{3}/2 \approx 0.866$.
Solution

Range for a throw at an angle to the horizontal:

$$L = \frac{v_0^2 \sin 2\alpha}{g}$$

$$L = \frac{15^2 \cdot \sin 60°}{10} = \frac{225 \cdot 0.866}{10} \approx 19.5 \text{ m}$$

Answer

$L \approx 19.5$ m