In its final trip upstream to its spawning territory, a slamon jumps to the top of a waterfall 1.9m high. What is the minimum vertical velocity needed by the salmon at the end of this motion?
please, please help me answer this!
The exact same speed that it would have at the bottom if it fell 1.9 m instead of jumping up.
We already did a falling problem yesterday.
To find the minimum vertical velocity needed by the salmon at the end of its motion, we can use the principle of conservation of energy. The salmon will need enough vertical velocity to overcome the gravitational potential energy associated with its height above the water.
The gravitational potential energy (PE) of an object near the Earth's surface is given by the equation:
PE = m * g * h
Where:
- m is the mass of the object
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height above a reference point (in this case, the water level)
Since we are looking for the minimum vertical velocity, we can assume that there is no additional energy loss due to air resistance.
Now, let's find the minimum velocity needed by the salmon.
First, we need to determine the mass of the salmon. For the purpose of this explanation, we'll assume a mass of 1 kg.
Next, we plug in the values into the equation:
PE = 1 kg * 9.8 m/s^2 * 1.9 m
Simplifying the equation, we get:
PE = 18.62 J
The potential energy is equal to the kinetic energy at the top of the jump:
PE = KE
We can use the equation for kinetic energy (KE) to solve for velocity:
KE = 1/2 * m * v^2
Where:
- v is the velocity
Rearranging the equation, we have:
v^2 = (2 * PE) / m
Plugging in the values:
v^2 = (2 * 18.62 J) / 1 kg
Simplifying,
v^2 = 37.24 m^2/s^2
Finally, taking the square root of both sides, we find:
v ≈ 6.1 m/s
Hence, the minimum vertical velocity needed by the salmon at the end of the motion is approximately 6.1 m/s.