If a 71.0 kg , 1.70 m -tall human could jump to the same height compared with his length as the flea jumps compared with its length, how high could he jump, and what takeoff speed would he need?
height=1.7 x ?? my guess is 40x
then velocity is equal ...
v^2=2*h*9.8
solve for takeoff velocity v
To answer this question, let's first understand the jumping ability of a flea relative to its size.
Fleas are known for their incredible jumping ability. They can jump up to 150 times their body length. This means that if a flea is 1 centimeter long, it can jump up to 150 centimeters or 1.5 meters. We will use this information to determine the height that a human could jump if they had the same jumping ability relative to their size.
Now, let's calculate the height a human could jump using the same ratio. The question mentions that the human is 1.70 meters tall. We need to find 150 times the human's body length. Given that the average human body length is approximately equal to their height, we can multiply 1.70 meters by 150.
Height = 1.70 meters * 150 = 255 meters
Therefore, if a human had the same jumping ability as a flea relative to its size, they could jump approximately 255 meters.
Now, let's move on to calculating the takeoff speed required for this jump. To make this calculation, we will use the principles of physics and conservation of energy.
When jumping, an object converts its potential energy into kinetic energy. The potential energy gained from a jump is equal to the product of the object's mass (m), gravitational acceleration (g), and height (h) reached.
Potential Energy (PE) = m * g * h
In this case, the mass (m) of the human is given as 71.0 kg, the gravitational acceleration (g) is approximately 9.8 m/s^2, and the height (h) is 255 meters.
PE = 71.0 kg * 9.8 m/s^2 * 255 meters
= 174,615 Joules
Now, let's calculate the kinetic energy at takeoff using the principle of conservation of energy. The kinetic energy (KE) is equal to the potential energy (PE) gained.
KE = PE
The kinetic energy is given by the formula:
KE = (1/2) * m * v^2
Where v represents the takeoff speed.
Setting the potential energy and kinetic energy equal to each other:
(1/2) * m * v^2 = 174,615 Joules
Rearranging the equation to solve for v:
v^2 = (2 * PE) / m
v^2 = (2 * 174,615 Joules) / 71.0 kg
v^2 = 4,921.197 Joules / kg
Taking the square root of both sides to solve for v:
v ≈ 70.196 m/s
Therefore, to jump to the height equivalent to a flea's jump relative to its size, the human would need a takeoff speed of approximately 70.196 m/s.