Question 144: Motion in 2D & Vectors

Question

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m . The speed of the bullets from the gun is $\_\_\_\_$ $\mathrm{m} / \mathrm{s}$.
$$ 	ext { (take } \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 	ext { ) } $$

Accepted Answer

For a projectile fired from the ground with speed $u$, the horizontal range is
$$ R=\frac{u^2\sin 2	heta}{g} $$
The
maximum range
occurs when
$$ \sin 2	heta = 1 $$
So,
$$ R_{\max}=\frac{u^2}{g} $$
Given:
$$ R_{\max}=6.4\ 	ext{m}, \qquad g=10\ 	ext{m/s}^2 $$
Substitute:
$$ 6.4=\frac{u^2}{10} $$
$$ u^2=64 $$
$$ u=8\ 	ext{m/s} $$
So, the speed of the bullets is
$$ \boxed{8\ 	ext{m/s}} $$

Motion in 2D & Vectors

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m . The speed of the bullets from the gun is \_\_\_\_ \mathrm{m} / \mathrm{s}. $ \text { (take } \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 \text { ) }

Integer / Numeric Answer Type