Question

An archer on the roof of a tower shoots an arrow at a bird in flight. The arrow travels at 255 m/s. The bird is directly across from the archer at a distance of 90.0 m. The archer misses. If the tower is 200 m tall and if we assume the cow is at ground level, will his stray arrow hit the cow? (The cow is 145 m away from the tower.)

Answer 1

consider the motion along the Y-direction

V_oy = initial velocity = 0 m/s (since the arrow was launched horizontally)

a = acceleration = - 9.8

Y = vertical displacement = height of the tower= - 200 m

t = time of travel = ?

using the equation

Y = V_oy t + (0.5) a t²

- 200 = 0 t + (0.5) (- 9.8) t²

t = 6.4 sec

consider the motion along the X-direction

V_ox = initial velocity = 255 m/s

X = horizontal displacement = ?

using the equation

X = V_ox t

X = 255 x 6.4

X = 1632 m

hence the arrow hits the cow