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 630 with respect to the water surface.
A. Find an expression for how fast the drop is moving when it leaves the fish's mouth. (Your expression should only contain symbols of physical quantities. No numbers are needed here. )
B. Find the numerical value for how fast the drop is moving when it leaves the fish's mouth. (Plug the values of physical quantities into your expression from part A (do not forget units!) Evaluate your answer that you found in part B by using it to find the value of a physical quantity given in the problem statement. (This is called evaluating for consistency.) For instance, suppose you knew the initial speed of the water (i.e., your answer in part B), the launch angle ( 63º) and the grasshopper's initial horizontal position (0.25 m). Using this information, find the initial vertical position of the grasshopper. Is this value consistent with the value given in the problem statement?

Answer 1

Answer:

Explanation:

Let the required velocity be V   at angle θ with the horizontal . Let time taken in the whole process be t

horizontal component = v cosθ

It will cover .25 m at this velocity

vertical component = v sinθ

It will cover .45 m with this initial velocity and with deceleration g .

v cosθ t = .25

.45 =v sinθ t - 1/2 g t²

putting the values of t from above

.45 = .25 tanθ - g .25² / 2 v² cos²θ

B ) putting the values of θ

.45 = .25 tan63 - 9.8 x .25² / 2 v² cos² 63

.45 = .49 - 1.53 / v²

1.53 / v² = .04

v² = 38.25

v = 6.18 m /s

time taken to cover distance of .25 m

t = .25 / 6.18 cos63 = .089 s

during this period , vertical displacement

= 6.18 sin 63 x .089  - 1/2 x 9.8 x .089²

= .4895 - .04  = .45 m which is consistence with given height .