An archer lines up an arrow on the horizontal exactly dead center on a target as

Question

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 = 7.85 cm below the center. If the target is 12 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

Explanation / Answer

h = 7.85cm

a) for the time of flight t

Using second equation of motion

h = 0.50 * g * t^2

0.0785 = 0.50 * 9.8 * t^2

t = 0.127 s

the time of flight is 0.127 s

b) initial velocity = horizontal distance/t

initial velocity = 12/.127

initial velocity = 94.8 m/s

initial velocity = 94.8/.3048 feet/s = 311 feet/s

initial velocity = 94.8 * 3600/1609 miles per hour

initial velocity = 212 milesper hour

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