Question

You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. You find the arrow stuck in the ground 61.0 m away, making a 2.00 ∘ angle with the ground?

Answer 1

Answer:

Velocity of throwing arrow = 43.13 m/s.

Explanation:

In the question,

Let us say the height from which the arrow was shot = h

Distance traveled by the arrow in horizontal = 61 m

Angle made by the arrow with the ground = 2°

So,

From the equations of the motion,

$61 =u.t\\t=\frac{61}{u}$

Now,

Also,

Finally, the angle made is 2 degrees with the horizontal.

So,

Final horizontal velocity = v.cos20°

Final vertical velocity = v.sin20°

Now,

u = v.cos20° (No acceleration in horizontal)

Also,

$v=u+at\\vsin20=0+9.8(t)\\t=\frac{v.sin20}{9.8}$

So,

We can say that,

$\frac{v.sin20}{9.8}=\frac{61}{v.cos20}\\v^{2}.sin20.cos20=597.8\\v^{2}=1860.56\\v=43.13\,m/s$

Therefore, the velocity with which the arrow was shot by the archer is 43.13 m/s.