A pole-vaulter of mass 59.9 kg vaults to a height of 5.9 m before dropping to thick padding placed below to cushion her fall.
(a) Find the speed with which she lands.
m/s
(b) If the padding brings her to a stop in a time of 0.48 s, what is the average force on her body due to the padding during that time interval?
N
I have no clue how to even start this! If someone could help, then please; I would appreciate it!
a. find the speed from the height he fell.
b. force*time=mass(changeinVelocityatImpact)
Do I use kinematic equation for part a?
And what would be the force for part b?
Thank you!
From the law of conservation of energy:
PE = KE
mgh = mv^2/2
v=sqr(2gh)=sqr(2•9.8•5.9)=10.75 m/s
F=ma=m•Δv/Δt=59.9•10.75/0.48=1342 N
Thank you Elena :) !
To find the speed with which the pole-vaulter lands, we can use the principle of conservation of energy. At the highest point of the vault, all of the pole-vaulter's energy is potential energy, given by the equation:
Potential Energy = Mass * Gravity * Height
Where:
Mass = 59.9 kg (mass of the pole-vaulter)
Gravity = 9.8 m/s² (acceleration due to gravity)
Height = 5.9 m (height reached by the pole-vaulter)
Substituting these values into the equation, we get:
Potential Energy = 59.9 kg * 9.8 m/s² * 5.9 m
Now, we can equate the potential energy to the final kinetic energy when the pole-vaulter lands. The kinetic energy is given by:
Kinetic Energy = 0.5 * Mass * Velocity²
Since the pole-vaulter lands and comes to rest (velocity becomes zero), the final kinetic energy is zero. Equating the potential energy to zero, we can solve for the velocity.
Potential Energy = Kinetic Energy
59.9 kg * 9.8 m/s² * 5.9 m = 0.5 * 59.9 kg * Velocity²
Now, solve for Velocity:
Velocity² = (2 * 9.8 m/s² * 5.9 m) / 59.9 kg
Velocity² = 1.96 m²/s²
Velocity = √(1.96 m²/s²)
Therefore, the speed with which the pole-vaulter lands is approximately 1.4 m/s. (a) = 1.4 m/s
To calculate the average force on her body due to the padding, we can use Newton's second law, which states that force is equal to mass times acceleration.
Force = Mass * Acceleration
In this case, the acceleration can be found by dividing the final velocity (zero) by the time, according to the equation:
Acceleration = Velocity / Time
Since the pole-vaulter lands and comes to rest, the final velocity is zero. Substituting this information:
Acceleration = 0 m/s / 0.48 s
Now, we have both the mass of the pole-vaulter and the acceleration. We can calculate the average force:
Force = 59.9 kg * 0 m/s / 0.48 s
Force = 0 N
Therefore, the average force on the pole-vaulter's body due to the padding during the time interval is zero. (b) = 0 N