i dont know what the answer is... i got itwrong my answer was 1.78. whats the correct answer?
A 57kg trampoline artist jumps vertically upward from the top of a platform with a speed of 4.7m/s. How fast is he going as he lands on the trampoline 3.8m below?
his final KE=KE at launch + PE at launch
1/2 mv^2=1/2 m 4.7^2 + m(9.8)(3.8)
V^2=44+37
v= 9m/s
his mass has nothing to do with it.
Vi = 4.7
how long to reach top?
v = Vi - g t
0 = 4.7 - 9.81 t
t = .479 seconds up
H = 3.8 + Vi t - 4.9 t^2
h = 3.8 + 4.7(.479) - 4.9 (.479^2)
h = 3.8 + 2.25 - 1.12
h = 4.93 meters stopped above ground, falls from there
4.93 = 4.9 t^2
t = 1 second fall from 4.93 meters
v = g t = 9.81 * 1 = 9.81 m/s
which one of you are correct?
To find the speed of the trampoline artist as he lands on the trampoline, we can use the principle of conservation of energy and apply it to this situation.
The conservation of energy states that the total mechanical energy of a system remains constant, assuming there are no external forces or non-conservative forces involved. In this case, we can assume there are no significant air resistance or energy losses, so we can assume conservation of energy.
Initially, the trampoline artist has gravitational potential energy due to his position above the ground and kinetic energy due to his initial speed. Finally, when he lands on the trampoline, all of his initial kinetic energy will be converted into potential energy as he reaches the maximum height of the bounce.
Let's break this down step by step:
1. Calculate the initial potential energy:
The initial potential energy is given by the equation: Potential Energy = mass * gravity * height
Here, the mass of the trampoline artist is 57 kg, the acceleration due to gravity is approximately 9.8 m/s^2, and the initial height above the trampoline is zero (since he is on the platform). Therefore, the initial potential energy is 0 J.
2. Calculate the initial kinetic energy:
The initial kinetic energy is given by the equation: Kinetic Energy = 0.5 * mass * velocity^2
Using the given mass of 57 kg and the initial velocity of 4.7 m/s, we can calculate the initial kinetic energy. Plugging in the values, the initial kinetic energy is approximately 760.77 J.
3. Calculate the final potential energy:
At the maximum height of the bounce (when the trampoline artist is momentarily at rest before falling back down), all of the initial kinetic energy is converted into potential energy.
Therefore, the final potential energy is equal to the initial kinetic energy, which is approximately 760.77 J.
4. Calculate the final kinetic energy:
When the trampoline artist lands on the trampoline, the final potential energy is converted back into kinetic energy. Since the final potential energy is the same as the initial kinetic energy, the final kinetic energy is also approximately 760.77 J.
5. Calculate the final speed:
The final speed can be found using the equation: Final Speed = √(2 * final kinetic energy / mass)
Plugging in the values, the final speed is approximately 5.14 m/s.
Therefore, the correct answer is approximately 5.14 m/s.
I hope this explanation helps you understand how to find the correct answer!