Answer to Question #91859 in Mechanics | Relativity for Sarah

Question

Calculate the distance an arrow will land from a hunter if he releases the arrow
with a speed of 20m/s at a 60 degree angle above the horizontal. The tip of the
arrow is 1.5 m above the ground at the point of release.

Answer 1

the maximum height at which the arrow will fly relative to its tip

$H=\frac{u^2\times\sin^2(\alpha)} {2\times g}$

u - initial speed;

α - angle to the horizontal;

g -acceleration of gravity (10 m/s^2);

H= 15 m;

the time of flight of an arrow to its maximum height (from tip):

$t=\sqrt{\frac{2 \times H}{g}}$

t≈1.73 s;

the time of flight of an arrow from the maximum height to the ground:

$T=\sqrt{\frac{2 \times (H+h)}{g}}$

h-the initial height of the tip;

T≈1.82;

the distance at which the arrow falls:

$L=u\times\cos(\alpha)\times(t+T)$

L≈35.5m

Answer 35.5m