Hi, I need the answer to the following questions PROBLEM 1 PROBLEM 2 In a partic

Question

Hi, I need the answer to the following questions

PROBLEM 1

PROBLEM 2

In a particular Cartesian coordinate system, a particle has coordinates
x(t) = 2sin(3t) + C, y = 0, z = 0,
where t is in seconds, x is in meters, and C is a constant to be determined by the data. At t = 0 the particle was at x = 1 m.
Part (a) Find the value of constant C, in meters. Numeric : A numeric value is expected and not an expression. C =
__________________________________________  

Part (b) Find the instantaneous velocity, in meters per second, at t = 1.1 s. Numeric : A numeric value is expected and not an expression.vx(t1) = __________________________________________
Part (c) Find the instantaneous velocity, in meters per second, at t = 2.5 s. Numeric : A numeric value is expected and not an expression. v x(t2) = __________________________________________  
Part (d) Find the instantaneous velocity, in meters per second, at t = 2.7 s. Numeric : A numeric value is expected and not an expression. v x(t3) = __________________________________________  
Part (e) Find the instantaneous acceleration, in meters per square second, at t = 1.1 s. Numeric : A numeric value is expected and not an expression. a x(t1) = __________________________________________  
Part (f) Find the instantaneous acceleration, in meters per square second, at t = 2.5 s. Numeric : A numeric value is expected and not an expression. a x(t2) = __________________________________________  
Part (g) Find the instantaneous acceleration, in meters per square second, at t = 2.7 s. Numeric : A numeric value is expected and not an expression. a x(t3) = __________________________________________

Problem 1: A child fills a water gun in a pool. She holds the gun so the nozzle is submerged, just below the water's surface (as shown) and the gun tilted at an angle of -25° from the horizontal. She pulls on a handle at the lower end of the gun, which pulls a piston down along the length of the gun's cylindrical tank and sucks water into the tank through the nozzle. The tank's length is L-066 m. The density of water is - 1.00 x 10 kgm3 Otheexpertta.com Part (a) Enter an expression for the hydrostatic gauge pressure at the lower end of the gun's tank when it is full of water, in terms of the defined quantites Expression es and the acceleration due to gravity, g LS Select from the variables below to write your expression. Note that all variables may not be required. cos@), cos(p), cos(9), sin(), sin(p), sin(9-y, P. , g, L, m.n, t Part (b) Calculate the hydrostatic gauge pressure, in pascals, at the lower end of the gun's tank when it is full of water. Numeric :A mumeric value is expected and not an expression. LS Part (c) Now we investigate the dynamics of filling the water gun's tank. Assume the child pulls the plunger at a steady speed along the whole length L- 0.66 m of the tank during a time interval of t 6.1 s. Enter an expression for the dynamic gauge pressure at the lower end of the tanlk just as the piston is reaching the end of its travel. dyn Select from the variables below to write your expression. Note that all variables may not be required. cos@), cos(p), cos(9), sin(), sin(p), sin(9-y, P. , g, L, m, n, t Part (d) Calculate the dynamic gauge pressure, in pascals, at the lower end of the tank just as the piston is reaching the end of its travel. Numeric :A mumeric value is expected and not an expression.

Explanation / Answer

(a)

x(t) = 2sin(3t) + C

at t = 0 , x =1 put in above equation

1 = 0 + C

C = 1

(b)

instantaneous velocity v(t) = dx(t)/dt

x(t) = 2*sin(3t)

v(t) = d(2*sin(3t)) / dt

v(t) = 6cos(3t)

at t = 1.1 s

v(t) = 6*cos(3*1.1) = 6*cos(3.3) here angle is in radian.

v(t) = -5.92 m/s

(c)

at t = 2.5 s

v(t) = 6*cos(3*2.5) = 6*cos(7.5)

v(t) = 2.07 m/s

(d)

at t = 2.7 s

v(t) =6*cos(3*2.7) = 6*cos(8.1)

v(t) =  -1.46 m/s

(e)

instantaneous acceleration , a(t) = dv(t)/dt = -18*sin(3t)

at t = 1.1 s

a(t)= -18*sin(3*1.1)

a(t) = 2.83 m/s3

(f)

at t =2.5 s

a(t ) = -18*sin(3*2.5)

a(t) = - 16.88 m/s2

(g)

a(t) = -18*sin(3*2.7)

a(t) = - 17.45 m/s2

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