4.
1 answer:
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Answer:
The maximum height that the fish can jump is 2.19 m.
Explanation:
Hi there!
Please, see the attached figure for a better understanding of the problem.
The motion of the salmon is a parabolic one because when it jumps, it already has a horizontal velocity (see figure).
The position and velocity vectors of the salmon at a time t, can be calculated as follows:
r = (x0 + v0x · t, y0 + v0y · t + 1/2 · g · t²)
v = (v0x, v0y + g · t)
Where:
r = position of the salmon at time t.
x0 = initial horizotal position.
v0x = initial horizontal velocity.
t = time.
y0 = initial vertical position.
v0y = initial vertical velocity.
g = acceleration of gravity.
Looking at the figure, notice that at the maximum height, the vertical velocity is zero (because the velocity vector is horizontal). Using the equation of the vertical component of the velocity, we can obtain the time at which the salmon is at its maximum height:
vy = v0y + g · t
To find the initial vertical velocity, v0y, let´s look at the figure. Notice that the initial velocity is the hypotenuse of the triangle formed with the horizontal velocity and the vertical velocity. Then:
v0² = v0x² + v0y²
Solving for v0y:
v0y = √(v0² - v0x²)
v0y = √((6.75 m/s)² - (1.65 m/s)²)
v0y = 6.55 m/s
Now, using the equation of the vertical component of the velocity at the maximum height (vy = 0):
vy = v0y + g · t
0 = 6.55 m/s + (-9.8 m/s²) · t
-6.55 m/s / -9.8 m/s² = t
t = 0.67 s
Now, using the equation of the vertical position at t = 0.67 s, we can find the maximum height:
y = y0 + v0y · t + 1/2 · g · t²
y = 0 m + 6.55 m/s · 0.67 s + 1/2 · (-9.8 m/s²) · (0.67 s)²
y = 2.19 m
The maximum height that the fish can jump is 2.19 m.
Answer:
a)
b) Ball 1 has a greater speed than ball 2 when they are passing.
c) The height is the same for both balls = 3h/4.
Explanation:
a) We can find the time when the two balls meet by equating the distances as follows:
Where:
: is the initial height = h
: is the initial speed of ball 1 = 0 (it is dropped from rest)
(1)
Now, for ball 2 we have:
Where:
: is the initial height of ball 2 = 0
(2)
By equating equation (1) and (2) we have:
Where the initial velocity of the ball 2 is:
Since = 0 at the maximum height (h):
Hence, the time when they pass each other is:
b) When they are passing the speed of each one is:
For ball 1:
The minus sign is because ball 1 is going down.
For ball 2:
Therefore, taking the magnitude of ball 1 we can see that it has a greater speed than ball 2 when they are passing.
c) The height of the ball is:
For ball 1:
For ball 2:
Then, when they are passing the height is the same for both = 3h/4.
I hope it helps you!