10:27 AM ooo T-Mobile session masteringphysics.com C Item 9 Aboat of mass 250 ke
ID: 1438924 • Letter: 1
Question
10:27 AM ooo T-Mobile session masteringphysics.com C Item 9 Aboat of mass 250 ke is coasting, with its engine in neutral, through the water at speed 1.00 when it starts to rain with incredible intensity. The rain is falling vertically, and it accumulates in the boat at the rate of 100 kar Part A What is the speed of the boat after time 0.500 hr has passed? Assume that the water resistance is negligible. Express your answer in meters per second. Hints My Answers Give Up Review Part Part B Now assume that the boat is subject to a drag force F, due to water resistance. Is the component of the total momentum of the system parallel to the direction of motion still The boat is subject to an external force, the drag force due to water resistance, and therefore its momentum is not conserved. Part C The drag is proportional to the square of the speed of the boat, in the form F where os N. ma. What is the acceleration of the boat just after the rain starts? Take the positive a axis along the direction of motion. Express your answer in meters per second per second. 2.10 Submit Hints My Answers Give Up Review Part Incorrect: Ty Again: 2 attempts remainingExplanation / Answer
Make a momentum balance in the direction of motion (the x-direction).
The change of the momentum equals the forces acting on the boat. There is only the drag force, which acts against the direction of motion. :
d(m·v)/dt = -F_d = - k·v²
where k = 0.5 Ns²/m²
Expand the time derivative on the LHS, by applying product rule of differentiation:
v·dm/dt + m·dv/dt = - k·v²
where dm/dt = 100kg/hr is the change of the mass of the boat
The acceleration is the time derivative of time velocity:
a = dv/dt = - (k·v² + v·dm/dt) / m
For the moment,w hen the rain starts all the value on the right hand side are known, thus:
a = - (k·v² + v·dm/dt) / m
= - (0.5Ns²/m² · (1m/s)² + 3m/s · 100kg/3600s ) / 250kg = -2.33·10³ m/s²
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.