If a salmon swims straight upward in the water fast enough to break through the surface at a speed of 5 meters per second, how high can it jump above water?

Vi = 5 m/s

a = g = -9.81 m/s^2

v = Vi - 9.81 t
v = 0 at top
so
0 = 5 - 9.81 t
t = .51 seconds to top
h = Hi + Vi t + (1/2)a t^2
h = 0 + 5(.51) - 4.9 (.51)^2
h = 2.55 - 1.27
h = 1.28 meters

by the way I could have done that really quickly by saying that the average speed up was half the starting speed.

h = (1/2)(5)(.51) = 1.28

Why did the salmon want to jump out of the water? Because it heard it's fin-ished with all that swimming! *tosses confetti* Now, let's do some fishy math, shall we?

Assuming the salmon jumps straight up without any impediments, we can use a basic formula to estimate the height it can reach. The formula we'll use is h = (v^2) / (2g), where v is the velocity (5 m/s) and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Plugging in the values, we get: h = (5^2) / (2 * 9.8) = 12.76 meters above the water.

So, the salmon can jump approximately 12.76 meters above the water. That's quite a leap! I hope it doesn't get in trouble for scaling new heights.

To determine how high a salmon can jump above water, we need more information. Specifically, we need to know the initial velocity of the salmon when it breaks through the surface and any other factors that may affect its jump height, such as the salmon's body size, strength, or physiological characteristics.

To determine how high the salmon can jump above water, we need to consider the factors involved. In this case, we know the speed at which the salmon breaks through the surface, but we don't have enough information to determine the exact height it can reach. However, we can make an estimation based on some assumptions:

1. Assuming the salmon jumps with a constant speed: If the salmon swims upward at a speed of 5 meters per second and continues jumping at the same speed, it will continue to rise until the force of gravity slows it down and eventually brings it back down. The maximum height the salmon can reach can be calculated using basic kinematic equations.

2. Assuming negligible air resistance: If we neglect air resistance, the only force acting on the salmon will be gravity. This means that during its upward motion, the salmon will decelerate due to the effects of gravity until it reaches its highest point, at which it momentarily comes to rest before descending back down.

To calculate the maximum height the salmon can reach, we can use the following kinematic equation:

vf^2 = vi^2 + 2ad

Where:
- vf is the final velocity (0 m/s at the highest point, as the salmon comes to rest momentarily)
- vi is the initial velocity (5 m/s, as given in the question)
- a is the acceleration (due to gravity, approximately -9.8 m/s^2 since it acts in the opposite direction to the salmon's motion)
- d is the displacement or height reached by the salmon.

Rearranging the equation, we get:

d = (vf^2 - vi^2) / (2a)

Since the final velocity (vf) is 0 m/s at the highest point, the equation simplifies to:

d = (0 - vi^2) / (2a)

Plugging in the values, we have:

d = (0 - 5^2) / (2 * -9.8)

Calculating further:

d = -25 / -19.6

d ≈ 1.28 meters

Therefore, based on our assumptions, the salmon can jump approximately 1.28 meters above the water's surface.