William tell must split the apple atop his son's head from a distance of 24 m. when he aims directly at the apple, the arrow is horizontal. at what angle must he aim it to hit the apple if the arrow is shot at a speed of 25.1 m/s? (find the smaller of two possible angles.)

Let x = the angle of elevation for shooting the arrow.

Assume

g = 9.8 m/s²

No wind resistance

The vertical launch velocity is 25.1 sin (x) m/s

The horizontal velocity is 25.1 cos (x) m/s

The time of flight is

24/[25.1 cos (x) ] s = 0.9562 sec (x) s

Therefore

0.5*[0.9562 sec (x) ] * (9.8) = 25.1 sin (x)

4.6854 = 25.1 * sin (x) cos (x)

sin (2x) = 0.3733

2x = sin⁻¹ 0.3733 = 21.92 deg

x = 10.96 deg

Answer: 11 degrees (nearest integer)