Question

A hunter aims directly at a target (on the same level) 36.0 m away.

a, If the arrow leaves the bow at a speed of 22.8 m/s , by how much will it miss the target?

b, At what angle should the bow be aimed so the target will be hit?

Answer 1

Using x = vt

where x is horizontal distance, v is velocity and t is time

t = x / v

t = 36 / 22.8

t = 1.578 sec

this is time in air.

How much the object has moved vertically in this time

y = 1/2gt²

y = 1/2 * 9.8 * 1.578²

y = 12.2 m ( below target)

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(b) Here, we can use range equation for projectile motion

R = v² sin 2$\theta$ / g

sin 2$\theta$ = Rg / v²

sin 2$\theta$ = 0.6786

2$\theta$ = 42.739

$\theta$ = 21.36 degree