An obnoxious brat assigns his 0.0221-kilogram pet mouse Mickey the role of stunt mouse by stuffing him into a spring gun and shooting him up into the air at some angle. During the launch process the spring transfers 0.707 J of energy into the \'mouse Earth gravitational fields\' system. When Mickey reaches his maximum height, he has a horizontal velocity with a speed of 2.37 m/s. How high above his initial location in the gun does Mickey soar? (In case you are worried, a miniature parachute opens at this point and Mickey lands safely. The brat is slightly less obnoxious than we thought.) Take g = 9.81 m/s2.
can somebody work it out to show me not just give the formulas, please , thanks
Use the excerpt from the Civil Rights Act of 1964 to answer the question.
Which of the following did NOT help lead to the passage of this act in the decade prior to its passage? EXPLAIN
A. sit-ins
B. protests
C. mass public demonstrations
D. official school segregation
D. Official school segregation did not help lead to the passage of the Civil Rights Act of 1964. This act was passed to prohibit discrimination on the basis of race, color, religion, sex, or national origin in employment, voting rights, and public accommodations. The official school segregation, on the other hand, was ruled unconstitutional in the landmark case Brown v. Board of Education in 1954. While the decision was met with resistance in some parts of the country, it did not play a direct role in the passage of the Civil Rights Act a decade later.
Sure! To determine the height above Mickey's initial location, we can use conservation of energy. Let's break down the problem step by step.
1. Calculate the potential energy (PE) gained by Mickey at his maximum height:
PE = mgh
Where:
- m is the mass of Mickey (0.0221 kg)
- g is the acceleration due to gravity (9.81 m/s^2)
- h is the height we want to find
2. Calculate the kinetic energy (KE) at Mickey's maximum height:
KE = (1/2)mv^2
Where:
- v is the horizontal velocity of Mickey at maximum height (2.37 m/s)
- m is the mass of Mickey (0.0221 kg)
3. Apply the conservation of energy principle:
The total energy at the maximum height is equal to the initial energy transferred by the spring:
Total energy = PE + KE = 0.707 J
4. Substitute the equations for PE and KE into the conservation of energy expression:
mgh + (1/2)mv^2 = 0.707 J
5. Rearrange and solve for h:
gh = (0.707 J - (1/2)mv^2) / m
h = [(0.707 J - (1/2)mv^2) / m] / g
Let's plug in the given values and calculate:
h = [(0.707 J - (1/2)(0.0221 kg)(2.37 m/s)^2) / 0.0221 kg] / 9.81 m/s^2
Simplifying the equation:
h = [(0.707 J - 0.026 J) / 0.0221 kg] / 9.81 m/s^2
h = (0.681 J / 0.0221 kg) / 9.81 m/s^2
h ≈ 30.990 m
Therefore, Mickey soars approximately 30.990 meters above his initial location in the gun.