An archer lines up an arrow on the horizontal exactly dead c

An archer lines up an arrow on the horizontal exactly dead center on a target as drawn in Figure P4.70. She releases the arrow and it strikes the target a distance h = 7.5 cm below the center. If the target is 9 m from the archer

(a) how long was the arrow in the air before striking the target.

(b) What was the initial velocity of the arrow as it left the bow? Report your answers in meters per second, feet per second and miles per hour. Neglect air resistance.

In meters per second?

In feet per second?

In miles per hour

Solution

a)

consider the motion along the Y-direction

Y = displacement = - h = - 7.5 cm = - 0.075 m

V_oy = initial velocity along the Y-direction = 0 m/s

a = acceleration = - 9.8 m/s²

t = time of travel

using the equation

Y = V_oy t + (0.5) a t²

- 0.075 = 0 t + (0.5) (- 9.8) t²

t = 0.124 sec

b)

along the X-direction

V_{ox =} velocity along the horizontal direction

X = distance travelled = 9 m

using the equation

X = V_ox t

9 = V_ox (0.124)

V_ox = 72.6 m/s

V_ox = 238.2 ft/s

V_ox = 162.4 mph