A rifle that shoots bullets at 438 m/s is to be aimed at a target 46.7 m away. I

Question

A rifle that shoots bullets at 438 m/s is to be aimed at a target 46.7 m away. If the center of the target is level with the rifle, how high (in cm) above the target must the rifle barrel be pointed so that the bullet hits dead center?

Explanation / Answer

x = (vo)(cos?)(t) [1] y = (vo)(sin?)(t) - (1/2)gt² 0 = (vo)(sin?)(t) - (1/2)gt² (1/2)(g)(t) = (vo)(sin?) [Lose solution of t = 0; this will not be when the bullet hits the target.] t = 2(vo)(sin?) / g Substitute t into [1]: x = (vo)(cos?)[2(vo)(sin?) / g] x = (vo)²(2sin?cos?) / g x = (vo)²sin(2?) / g 46.7 m = (438 m/s)²sin(2?) / (9.81 m/s²) sin(2?) = 0.00238 2? = 0.136° ? = 0.068° [Or, trying to hit the target the hard way, 2? = 180 - 0.136° -> ? = 89.93° ] "how high (in cm) above the target must the rifle barrel be pointed so that the bullet hits dead center?" To answer this question, we have to know the length of the rifle. If it's 1 m long, the muzzle would need to be sin0.068° = 8.7e-4 m or 0.087 cm above the butt of the rifle

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.