A 65 kg student consumes 2500 Cal each day and stays at the same weight. For three days in a row, while visiting his parents, she eats 3500 Cal and, wanting to keep from gaining weight decides to "work off" the excess by jumping up and down.
With each jump, he accelerates to a speed of 3.2 m/s before leaving the ground.
a) How high will he jump each jump?
b) How many jumps must he do to keep his weight? (body efficiency= 25%)
c) Is this a reasonable way not to gain weight?
d) What other ways can the student keep his weight?
how high: KE=mgh
h= (1/2 * 65*3.2^2 )/(65*9.8)=.52m...
jumps=(2500C*.25*1000c/C*4.18J/c )/(1/2*65*3.2^2)=7850
@bobpursley
Which formula did u use to obtain this
jumps=(2500C*.25*1000c/C*4.18J/c )/(1/2*65*3.2^2)
a) To determine how high the student will jump, we can use the principle of conservation of energy. The work done by the student to jump is equal to the gravitational potential energy gained.
Work done = Change in gravitational potential energy
The work done is given by the formula:
Work done = Force x Distance
= mass x acceleration x distance
Given:
mass = 65 kg
acceleration = 9.8 m/s^2 (acceleration due to gravity)
acceleration before leaving the ground = 3.2 m/s
From the equation of motion: v^2 = u^2 + 2as, where v = final velocity, u = initial velocity, a = acceleration, and s = displacement (height in this case).
We can rearrange the equation to solve for displacement:
s = (v^2 - u^2) / (2a)
Substituting the values:
s = (0 - (3.2)^2) / (2 x (-9.8)) [negative sign because the acceleration is opposite to the displacement]
s ≈ 0.537 m
Therefore, the student will jump approximately 0.537 meters high each jump.
b) To determine the number of jumps the student must do to keep his weight, we need to calculate the excess energy consumed and convert it into the work done by jumping.
Excess energy consumed = Total calorie intake - Normal calorie intake
= (3500 Cal x 3 days) - (2500 Cal x 3 days)
= 10,500 Cal - 7,500 Cal
= 3000 Cal
To convert calories into work, we need to multiply it by the efficiency factor of the body, which is 25%. The efficiency factor accounts for the fact that not all the calories consumed are converted into useful work.
Work done = Excess energy consumed x Efficiency factor
Substituting the values:
Work done = 3000 Cal x 0.25
= 750 Cal
Now, we need to convert the work done into the number of jumps using the formula:
Work done = Force x Distance
From part a, we know the height jumped is 0.537 m. Therefore, the distance covered during each jump is twice the height, i.e., 2 x 0.537 m = 1.074 m.
Substituting the values:
Work done = Force x Distance
750 Cal = Force x 1.074 m
To find the force, we can use the formula:
Force = mass x acceleration
Given:
mass = 65 kg
acceleration = 9.8 m/s^2 (acceleration due to gravity)
Substituting the values:
750 Cal = (65 kg x 9.8 m/s^2) x 1.074 m
Now, we can solve for the number of jumps:
Number of jumps = Work done / (Force x Distance)
Number of jumps = 750 Cal / ((65 kg x 9.8 m/s^2) x 1.074 m)
Calculating this, we get the approximate number of jumps the student must do to keep his weight.
c) While jumping can burn calories and help with weight management, it is not a reasonable method to solely rely on for preventing weight gain. Jumping up and down alone cannot provide a balanced exercise routine that targets all muscle groups or promotes cardiovascular fitness. Maintaining weight requires a combination of healthy eating habits, regular exercise, and overall lifestyle choices.
d) The student can keep his weight by adopting a few other ways, such as:
1. Balancing his calorie intake and expenditure: Consuming the same amount of calories as he burns through daily activities and exercise can help maintain weight. This can be achieved by tracking calorie intake, planning meals, and incorporating physical activity.
2. Engaging in regular exercise: A combination of cardiovascular exercises (such as running, cycling, or swimming) for 150 minutes per week, strength training exercises, and flexibility training can help maintain weight and improve overall fitness.
3. Choosing nutritious food: Incorporating a balanced diet consisting of lean proteins, whole grains, fruits, vegetables, and healthy fats can provide essential nutrients while controlling calorie intake.
4. Monitoring portion sizes: Being mindful of portion sizes can prevent overeating and help maintain weight. Using smaller plates and bowls, eating slowly, and listening to the body's hunger and fullness cues can be helpful strategies.
5. Managing stress levels: High levels of stress can lead to emotional eating or overeating. Finding healthy ways to manage stress, such as practicing relaxation techniques, engaging in hobbies, or seeking support, can contribute to weight maintenance.
It's essential to consult with a healthcare professional or a registered dietitian for personalized advice and recommendations based on individual circumstances.