Could you just explain part where they integrate the x and y components to get those equations

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter2: Newtonian Mechanics-single Particle
Section: Chapter Questions
Problem 2.51P: Let us make the (unrealistic) assumption that a boat of mass m gliding with initial velocity v0 in...
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Could you just explain part where they integrate the x and y components to get those equations
Problem 1-2D gravity and drag.
At time t = 0, a box with mass M = 10 kg is launched from a helicopter, moving at constant horizontal velocity Vhel = 10 m/s. The initial velocity of the box is
Vyo = 0. The height of the helicopter with respect to a plateau underneath is yo = 5.0 x 10² m, and its x-coordinate at time t = 0 is xo = 0. As the box falls, it is
subject to the force of gravity (assume g = 10 m/s2) and to the drag force Fo= -bv, with drag coefficient b = 10 kg/s. (a) Find the solution v(t) for the box
velocity (x and y components) as a function of time. (b) Estimate the time it takes for the box to reach the plateau at y = 0. (c) Estimate the maximum value
of x reached by the box.
(a) M du = My - bu
1
V₂(0)=Vhel
Vy(0)=0
dt I
dung bay
solving for v₂(t): v₂(t)=₁²²₂
solving for vylt): vy(t)= v₁(1-25/26)
(h) The free to i Y-H 10
where To = H
= M₂
where v=
Transcribed Image Text:Problem 1-2D gravity and drag. At time t = 0, a box with mass M = 10 kg is launched from a helicopter, moving at constant horizontal velocity Vhel = 10 m/s. The initial velocity of the box is Vyo = 0. The height of the helicopter with respect to a plateau underneath is yo = 5.0 x 10² m, and its x-coordinate at time t = 0 is xo = 0. As the box falls, it is subject to the force of gravity (assume g = 10 m/s2) and to the drag force Fo= -bv, with drag coefficient b = 10 kg/s. (a) Find the solution v(t) for the box velocity (x and y components) as a function of time. (b) Estimate the time it takes for the box to reach the plateau at y = 0. (c) Estimate the maximum value of x reached by the box. (a) M du = My - bu 1 V₂(0)=Vhel Vy(0)=0 dt I dung bay solving for v₂(t): v₂(t)=₁²²₂ solving for vylt): vy(t)= v₁(1-25/26) (h) The free to i Y-H 10 where To = H = M₂ where v=
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