The maximum range of a gun on horizontal surface is 16km. If g=10 ms-2, the muzzle velocity of the shell must be:-a. 1600 ms-1b. 400 ms-1c. 200 (root2 ) ms-1d. 160(root 10) ms-1I want the answer with full solution
Ananya Sharma , 9 Years ago
Grade 11
2 Answers
Akshay
Last Activity: 9 Years ago
maximum range will be when gun is shot at 45 deg. Lets prove this fact first, assume that gun is shot at angle a with horizontal with velocity v,
U = (v.cosa) i + (v.sina) j
s=U*t+0.5*a*t2 ,
a= – 10 j,
s = (v.cosa*t) i + (v.sina*t – 5.t2) j,
final y-coordinate will be 0,
so , t=v.sina / 5,
Range = v.cosa.t = v2.cosa . sina / 5 = v2 . sin2a /10,
The horizontal range will be maximum if the bullet is fired at an angle of 45° to the horizontal. We have, R=u^2*sin2β/g Since the angle is 45°,soR=u^2*(sin2*45°)/gor, R=u^2/gAlso, R=16km=16000mAnd, g=10m/s^2So, 16000=u^2/10or, u^2=16000*10or, u=√160000Therefore, u=400m/s Hope you understand this😊😊
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