As a prank, your friends have kidnapped you in your sleep, and transported you out onto the ice covering a local pond. Since you're an engineer, the first thing you do when you wake up is drill a small hole in the ice and estimate the ice to be 6.7cm thick and the distance to the closest shore to be 30.5 m. The ice is so slippery (i.e. frictionless) that you cannot seem to get yourself moving. You realize that you can use Newton's third law to your advantage, and choose to throw the heaviest thing you have, one boot, in order to get yourself moving. Take your weight to be 588 N. (Lucky for you that, as an engineer, you sleep with your knife in your pocket and your boots on.)
1)(a) What direction should you throw your boot so that you will most quickly reach the shore? away from the closest shore perpendicular to the closest shore straight up in the air at your friend standing on the closest shore
2)(b) If you throw your 1.08-kg boot with an average force of 391 N, and the throw takes 0.576 s (the time interval over which you apply the force), what is the magnitude of the force that the boot exerts on you? (Assume constant acceleration.)
391 N
3)(c) How long does it take you to reach shore, including the short time in which you were throwing the boot?
Just number 3
To calculate the time it takes for you to reach the shore, including the time taken to throw the boot, you can use the concept of impulse.
Impulse is defined as the change in momentum of an object and is equal to the force applied multiplied by the time interval over which the force is applied. In this case, the force applied is the force exerted by the boot and the time interval is given as 0.576 s.
Since impulse is equal to the change in momentum, we can use the equation:
Impulse = Change in momentum
The change in momentum can be calculated using the formula:
Change in momentum = Mass x Change in velocity
In this case, the mass of the boot is given as 1.08 kg and we need to find the change in velocity.
To find the change in velocity, we can use Newton's second law of motion, which states:
Force = Mass x Acceleration
Rearranging the equation, we get:
Acceleration = Force / Mass
Now we can calculate the acceleration using the given force and mass of the boot.
Once we have the acceleration, we can use the following kinematic equation to calculate the change in velocity:
Change in velocity = Acceleration x Time
Finally, we can substitute the calculated change in velocity into the equation for change in momentum to find the impulse.
Impulse = Mass x Change in velocity
Now that we have the impulse, we can calculate the time it takes for you to reach the shore by considering the initial momentum of the system (you and the boot) and the impulse.
Total initial momentum of the system = Mass of boot x initial velocity of boot + Mass of you x initial velocity of you
The final momentum of the system after you reach the shore would be zero since you come to rest.
Using the concept of conservation of momentum, we can relate the initial momentum and the impulse:
Total initial momentum of the system + Impulse = 0
Now we can solve for the time it takes to reach the shore by dividing the impulse by the total initial momentum of the system.
Time = -Impulse / Total initial momentum of the system
Please note that the negative sign is used because the direction of impulse and momentum are opposite in this scenario.
By following these steps, you can calculate the time it takes for you to reach the shore after throwing the boot.
your mass is ... 588 / g
the force (391 N) accelerates your mass for 0.576 s
find the acceleration ... f = m a ... a = f / m
find the distance during acceleration ... d = 1/2 a t^2
find your final velocity ... v = a t
time to shore = acceleration time +
... {[30.5 m -( acceleration distance)] / (final velocity)}