Question

An archerfish, peering from just below the water surface, sees a grasshopper standing on a tree branch that's just above the water. The archerfish spits a drop of water at the grasshopper and knocks it into the water. The grasshopper's initial position is 0.45 m above the water surface and 0.25 m horizontally away from the fish's mouth. The launch angle of the drop is 63° with respect to the water surface. Anticipating that the grasshopper would do this, the archerfish decides to spit the water at a higher speed but at the same launch angle (63°). At what speed should the archerfish spit the water for the drop to hit the grasshopper?

Answer 1

Answer:

Explanation:

let the velocity of throw is u .

Time to reach horizontally .25 m is equal to reach .45 m vertically

t = .25 / u cos63

= .55 / u

For vertical motion

- h = - ut + 1/2 gt²

-.45 = -usin63 x .55 / u + .5 x9.8 (.55 / u )²

-.45 = - .49 + 1.48 / u²

.04 = 1.48 / u²

u² = 37

u = 6.08  m /s

Answer 2

The archerfish should spit the water at a speed of $6.05\rm\;m/s$ to hit the grasshopper.

Given information:

The archerfish spits water to it the grasshopper. The motion of the water drop will be projectile.

The vertical distance of the grasshopper from the fish is $h=0.45$ m.

The horizontal distance of the grasshopper from the fish is $d=0.25$ m.

The angle of inclination of the droplet motion is $\theta =63^{\circ}$.

Let u be the initial velocity of the drop.

The time taken by the water to reach the grasshopper will be calculated as,

$t =\dfrac{d}{ucos\theta} \\t=\dfrac{0.25} { u cos63}\\t= \dfrac{0.5506}{ u}$

Now, the drop will move under the influence of gravity in the vertical direction. So, for vertical motion, the initial speed u can be calculated as,

$h = u_ht - \dfrac{1}{2} gt^2\\0.45=usin63^{\circ}\times \dfrac{0.5506}{u}-0.5\times 9.81(\dfrac{0.5506}{u})^2\\\dfrac{1.4873}{u^2}=0.04058\\u^2=36.64\\u=6.05\rm\;m/s$

Therefore, the archerfish should spit the water at a speed of $6.05\rm\;m/s$ to hit the grasshopper.

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https://brainly.com/question/11049671