Physics: force and motion

code PLUS

2012-04-11 10:36 pm

A barrel of a gun aims directly at a point P 40 m from the muzzle of the gun. The barrel makes an angle with the vertical. If the speed of the bullet is 50 m/s
when it leaves the gun, calculate the separation between the bullet and point P when the bullet is vertically below P.

(Neglect air resistance.)

A. 3.2 m
B. 4.8 m
C. 7.8 m
D. Cannot be found

~~Please show your steps clearly~~

回答 (1)

天同

2012-04-11 11:03 pm

✔ 最佳答案

Let a be the angle at which the barrel makes with the vertical.
Horizontal distance of the barrel from the point P = 40.sin(a)
Hence, 40.sin(a) = 50sin(a).t, where t is the time of flight for the bullet from the gun to a point vertically below P.
i.e. t = 40/50 s = 0.8 s

Consider the vertical motion, use equation: s = ut + (1/2)at^2
with u = 50.cos(a), t = 0.8 s, a = -g(=-10 m/s^2), s =?
s = [50.cos(a)].(0.8) + (1/2).(-10).(0.8^2) m = [40.cos(a) - 3.2] m

Hence, vertical separation between bullet and point P
= 40.cos(a) - [40.cos(a) - 3.2] m = 3.2 m
The answer is option A.

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