800 n student is standing in middle of frozen pond stranded 6.4 m from shore only thing he has is physics book which has mass of 3 kg so he throws it at 10 m/s toward one shore how long does it take him to reach opposite shore
speed s is found by conserving momentum:
800s = 3*10
time = 6.4/s
To determine how long it takes for the student to reach the opposite shore, we can use the principles of physics.
We can begin by analyzing the situation using the concept of conservation of momentum. The momentum of an object is given by the product of its mass and velocity. In this case, the student throws the physics book towards the shore, so we need to consider the momentum of both the student and the book separately.
The momentum of the student and the book should be equal and opposite in order to conserve momentum. Since the student is initially at rest, the momentum of the physics book must be equal in magnitude and opposite in direction to that of the student once the book is thrown.
The mass of the physics book is given as 3 kg, and the velocity with which it is thrown is 10 m/s. Therefore, the momentum of the book is calculated as:
Momentum of book = Mass of book × Velocity of book
= 3 kg × 10 m/s
= 30 kg·m/s
To maintain the conservation of momentum, the student's momentum should also be 30 kg·m/s, but in the opposite direction. Since the student is initially at rest, the final velocity of the student can be calculated using the equation:
Momentum of student = Mass of student × Velocity of student
30 kg·m/s = (mass of student) × (velocity of student)
Rearranging the equation to solve for velocity:
Velocity of student = 30 kg·m/s / (mass of student)
The mass of the student is 800 N (weight is given, assuming acceleration due to gravity is 9.8 m/s^2), and weight can be calculated using the equation:
Weight = Mass × Acceleration due to gravity
800 N = (mass of student) × 9.8 m/s^2
Rearranging the equation, we can solve for the mass of the student:
Mass of student = 800 N / 9.8 m/s^2
Now we can substitute the mass of the student into the equation for velocity:
Velocity of student = 30 kg·m/s / (800 N / 9.8 m/s^2)
Simplifying the equation, we get:
Velocity of student = (30 kg·m/s) × (9.8 m/s^2) / 800 N
Using a calculator, we can determine the velocity of the student.
Once we have the velocity of the student, we can calculate the time taken to reach the opposite shore. The distance between the student and the shore is given as 6.4 m. We can use the equation of motion:
Distance = Velocity × Time
Rearranging the equation to solve for time:
Time = Distance / Velocity
Substituting the known values into the equation:
Time = 6.4 m / (velocity of student)
Calculating this equation will give us the time taken for the student to reach the opposite shore.