How fast was the arrow shot??

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 degree angle with the ground.

you answer doesn't seem to be right...I dun know why though

Answer 1

Other answerers, please check my work.

Find the initial height of the arrow.
h = tan(2º) * 61.0 = 2.13 m

Find the time it took the arrow to fall 2.13 m. Since the archer is aiming parallel to the ground, this is the same time it would take the arrow to fall if it were dropped. In other words, the initial velocity in the y-direction is 0.

y = -½g t² + vy t + h

0 = -½(9.8)t² + 0t + 2.13

t = sqrt(-2.13/-4.9) = 0.659 s

Find the velocity in the x-direction. Since we're ignoring air resistance, the only force acting on the arrow is gravity. Gravity only acts in the y-direction. Since no forces are in the x-direction, there is no acceleration in the x-direction.

x = vx t
61 = vx * 0.659

vx = 61 / 0.659 = 92.56 m/s

If I made a mistake somewhere, please point it out to me.