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yuradex [85]
3 years ago
10

An object with mass of 4kg is thrown with initial velocity of 20m/s from point A and follows the track of ABCD.

Physics
1 answer:
soldier1979 [14.2K]3 years ago
5 0

<u>The distance of the length YD is 3.57m, the velocity of the object at point D is 27m/s and the time required for the object to reach the ground is 0.17s</u>

Data given;

  • Mass = 4kg
  • Initial velocity = 20m/s
  • length CD = 5m (from the image given)

a)

<h3>Determine The Length of YD</h3>

YD=CDsinθ = 5sin45=\frac{5}{\sqrt{2} } = 3.57m

b)

<h3>The velocity of the object at point D</h3>

The change in kinetic energy is given as

Δ in kinetic energy = Δ in potential energy + work done by friction

K.E - 1/2mv^2 = mgh_1 - mgh_2 + (-μmg.x)

K.E = mg(50 - 3.57) + (-mg(0.3*100) + 1/2 mv^2

\frac{1}{2}mv^2_f=mg(46.43)-mg(30)+\frac{1}{2} m(400)\\\\v^2_f=20(16.43)+400\\v^2_f=728.6\\v=\sqrt{728.6} \\v_f=26.99 = 27m/s

The velocity of the object at D with a distance of 5m.

c)

<h3>The the required for the object to reach ground</h3>

The velocity of the object in the y-axis is

v_y=vsin45=19.09

Acceleration in y-axis = 9.8

Height = 3.57m

h = ut+\frac{1}{2}at^2

3.57=19.28(t)+\frac{1}{2}(9.8)t^2\\3.57=19.28t+4.9t^2\\4.9t^2+19.28t-3.57=0\\a=4.9, b=19.28, c= -3.57\\t=\frac{-19.28+\sqrt{(19.28)^2-4(4.9)(-3.57)} }{(2*4.9)} \\t=\frac{-19.28+21.02}{9.8}

Taking the positive value

\frac{-19.28+21.02}{9.8}=0.17s

The time required for the object to reach ground is 0.17s

From the calculations above,<u> the distance YD is 3.57m, the velocity of the object at point D is 27m/s and the time required for the object to reach ground is 0.17s</u>

Learn more on projectile motion here;

brainly.com/question/1130127

<h3 />
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