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 68.0 m away, making a 3.00∘ angle with the ground. How fast was the arrow shot?

The speed of the arrow was 112.76 m/s

Explanation:

Angle the arrow made with the ground, ∅ = 3⁰

v = u tan∅ ... (1)

v = gt ... (2)

Equating (1) and (2)

gt = u tan ∅

t = (u tan ∅) / g ... (3)

g = 9.8 m/s²

Speed = (distance, s, covered by the arrow) / time taken

u = s/t

t = s/u ... (4)

Equating (3) and (4)

s/u = (u tan ∅) / g

Distance, s = 68m

68/u = (u tan 3°) / 9.8

9.8 * 68 = u² tan 3°

u² = (9.8 * 68) / tan 3°

u² = 666.4/0.0524

u² = 12715.67

u = √12715,67

u = 112.76 m/s