In its final trip upstream to its spawning territory, a salmon jumps to the top of a waterfall 1.9m high. What is the minimum vertical velocity neeeded by the salmon to reach the top of the waterfall?
this is the only info I have.
I did:
vf^2 = vi^2+2a∆d
0=vi^2+2(9.8)*1.9
vi^2 = = 2(9.8)*1.9
vi=√(37.24)
vi= 6.1m/s
is my answer correct?
works for me
V^2 = Vo^2 + 2g*h = 0,
Vo^2 + (-19.6)1.9 = 0,
Vo^2 - 37.24 = 0
Vo^2 = 36.24
Vo = 6.1 m /s.
Well, you know what they say about salmon and waterfalls - they really know how to make a splash! So, let's calculate the minimum vertical velocity needed for this daring salmon to reach the top of the waterfall.
To tackle this challenge, we can use the principles of physics. In this case, we'll rely on the concept of conservation of energy. As our smart salmon jumps, it initially has only gravitational potential energy. At the top of the waterfall, it reaches a maximum point with no kinetic energy.
The gravitational potential energy formula is given by:
PE = mgh
Where PE stands for the potential energy, m is the mass of the salmon, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the waterfall (1.9m).
Since the salmon reaches the top with no kinetic energy, all the initial energy must be gravitational potential energy. Thus, we can set the potential energy equal to zero at the top:
0 = mgh
Rearranging the equation, we find:
v^2 = 2gh
Where v is the vertical velocity of the salmon.
By plugging in the values, we get:
v^2 = 2 * 9.8 m/s² * 1.9m
Solving for v, we find:
v ≈ √37.24 m/s
Well, it seems our daring salmon needs a minimum vertical velocity of approximately √37.24 m/s to conquer this waterfall. That's quite a leap of faith!
To determine the minimum vertical velocity needed by the salmon to reach the top of the 1.9m high waterfall, we can utilize the principles of physics, specifically the laws of motion and conservation of energy.
The key principle we will employ here is the conservation of mechanical energy. In the absence of external forces like air resistance, the total mechanical energy remains constant throughout the salmon's motion.
The total mechanical energy of an object can be considered as the sum of its potential energy (PE) and kinetic energy (KE). The conservation of mechanical energy can be expressed as:
PE_initial + KE_initial = PE_final + KE_final
Since the salmon starts from the bottom of the waterfall and reaches the top, we can assume the initial kinetic energy (KE_initial) to be zero, as the salmon was initially at rest.
The total potential energy at the bottom of the waterfall (PE_initial) is given by:
PE_initial = m * g * h
where m is the mass of the salmon, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the waterfall (1.9m).
Thus, the conservation of mechanical energy equation simplifies to:
0 + 0 = m * g * h + KE_final
Since the salmon just reaches the top of the waterfall, its final potential energy (PE_final) will be zero.
Therefore, the equation becomes:
0 = m * g * h + KE_final
To find the minimum vertical velocity (V_vertical) needed by the salmon, we can calculate its final kinetic energy (KE_final) using the equation:
KE_final = 0.5 * m * V_vertical²
Applying these equations and rearranging, we get:
0 = m * g * h + 0.5 * m * V_vertical²
Simplifying and isolating V_vertical, we find:
V_vertical = √(2 * g * h)
Substituting the given values, we get:
V_vertical = √(2 * 9.8 * 1.9)
V_vertical = √37.24
V_vertical ≈ 6.11 m/s
Therefore, the minimum vertical velocity needed by the salmon to reach the top of the 1.9m high waterfall is approximately 6.11 m/s.