A nearsighted sheriff fires at a cattle rustler with his trusty six-shooter. For

Question

A nearsighted sheriff fires at a cattle rustler with his trusty six-shooter. Fortunately for the rustler, the bullet misses him and penetrates the town water tank, causing a leak.

(A) Find the speed of the water leaving the hole. Substitute P1 = P2 = P0 and v2 = 0 into Bernoulli's equation, and solve for v1. (B) Find where the stream hits the ground. Use the displacement equation to find the time of the fall, noting that the stream is initially horizontal, so v0y = 0. Compute the horizontal distance the stream travels in this time.

Explanation / Answer

let the water level is at height h above the hole then speed of water leaving the hole is v=sqrt(2*g*h) where g=9.8 m/s^2 now given that hole is 2.4 m above the ground as speed of water leaving the hole is along horizontal,the initial velocity along the vertical is 0. so time taken to reach ground=sqrt(2*height/g)=sqrt(2*2.4/9.8)=0.6999 sec so horizontal distance=horizontal speed*time taken to reach ground(as the acceleration along the horizontal=zero) ==>4.4=0.6999*sqrt(2*9.8*h) solving for h, we get h=2.0167 m so water level is 2.0167 m above the hole.

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