In the high jump, Frank's kinetic energy is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must Fran leave the ground in order to lift her center of mass 1.89m and cross the bar with a speed of 1.16m/s?
Answer:
1.27 m/s
Incorrect
The correct answer is: 6.20 m/s
someone please explain what i did....
when she crosses the bar she is moving in horizontal direction
Ux = 1.16 the whole time.
Now the vertical problem:
(1/2) m Vi^2 = m g h
so
Vi = sqrt (2gh) {This is worth remembering}
Vi = sqrt (2*9.81*1.89) = 6.09
so
|v| = sqrt (1.16^2+6.09^2) = 6.20 sure enough
Well, it seems like you didn't take into account the fact that Frank doesn't have a clown nose. You see, without a clown nose, Frank won't be able to generate the necessary lift to reach the desired height. It's a common mistake, really. The minimum speed required to lift her center of mass 1.89m and cross the bar is definitely in the range of 6.20 m/s, because as we all know, clowns can do some impressive jumps. So, just make sure to equip Frank with a clown nose next time, and everything will be fine!
To solve this problem, we can use the principle of conservation of energy. At the start of the high jump, Frank's kinetic energy will be converted into gravitational potential energy as she gains height.
The formula for gravitational potential energy is given by:
Potential Energy = mass x acceleration due to gravity x height
Since Frank's mass is not given, we can cancel it out as it appears in both the kinetic energy and potential energy formulas.
Given:
Height = 1.89 m
Final speed = 1.16 m/s
Acceleration due to gravity = 9.8 m/s^2
1. Initially, let's find the initial speed of Frank using the conservation of energy principle:
Kinetic Energy = Potential Energy
0.5 x mass x (initial speed)^2 = mass x 9.8 x 1.89
Simplifying gives:
0.5 x (initial speed)^2 = 9.8 x 1.89
2. Now, solve for the initial speed:
(initial speed)^2 = (9.8 x 1.89) / 0.5
(initial speed)^2 = 36.834
initial speed = √(36.834)
initial speed ≈ 6.06 m/s
So, the minimum speed Frank needs to leave the ground such that she lifts her center of mass 1.89 m and crosses the bar with a speed of 1.16 m/s is approximately 6.06 m/s.
It seems that there might have been an error in the calculation or rounding during the explanation you provided, which led to the incorrect answer of 1.27 m/s.
To solve this problem, we can use the principle of conservation of energy. The initial kinetic energy of Frank will be completely converted into gravitational potential energy at the maximum height of the jump.
Let's break down the steps to find the minimum speed Frank needs:
1. First, let's determine the gravitational potential energy at the maximum height:
- Gravitational potential energy (PE) = mass (m) * gravity (g) * height (h)
- PE = m * g * h
- Given that the maximum height (h) is 1.89m, and the acceleration due to gravity (g) is approximately 9.8 m/s^2, we can write the equation as:
PE = m * 9.8 * 1.89
2. Next, let's find the initial kinetic energy:
- Kinetic energy (KE) = 1/2 * mass (m) * velocity^2
- Given that the final speed (velocity) is 1.16 m/s, and we need to find the minimum initial speed, we can write the equation as:
KE = 1/2 * m * 1.16^2
3. According to the principle of conservation of energy, the initial kinetic energy should be equal to the gravitational potential energy at the maximum height:
KE = PE
1/2 * m * 1.16^2 = m * 9.8 * 1.89
4. Now we solve the equation for the mass (m):
1/2 * 1.16^2 = 9.8 * 1.89
0.6711792 = 18.522
This equation is incorrect.
Since the equation does not balance, the values given in the problem statement may be incorrect or there may be a mistake in the calculations.
However, the correct minimum speed to lift the center of mass 1.89m and cross the bar with a speed of 1.16m/s should be calculated using the conservation of momentum. The given answer of 6.20 m/s does not match the known equations for solving this problem.