<span>Answer:
So this involves right triangles. The height is always 100. Let the horizontal be x and the length of string be z.
So we have x2 + 1002 = z2. Now take its derivative in terms of time to get
2x(dx/dt) = 2z(dz/dt)
So at your specific moment z = 200, x = 100âš3 and dx/dt = +8
substituting, that makes dz/dt = 800âš3 / 200 or 4âš3.
Part 2
sin a = 100/z = 100 z-1 . Now take the derivative in terms of t to get
cos a (da./dt) = -100/ z2 (dz/dt)
So we know z = 200, which makes this a 30-60-90 triangle, therefore a=30 degrees or π/6 radians.
Substitute to get
cos (Ď€/6)(da/dt) = (-100/ 40000)(4âš3)
âš3 / 2 (da/dt) = -âš3 / 100
da/dt = -1/50 radians</span>
Answer:
Increases
Explanation:
The kinetic energy _____ (Increses)
as the roller coaster goes downhill
Answer:
Explanation: heat of fusion
49 J is the total kinetic energy. If a bowling ball of mass 7.3 kg and radius 9.6 cm rolls without slipping down a lane at 3.1 m/s. Kinetic energy is the energy an bowling ball has because of its motion.
Given: m = 7.3 Kg ; r = 9.4 cm = 0.094 m ; v = 3.1 m
Now total kinetic energy in this case is given by KE = Kinetic energy due to rotation + Kinetic energy due to translation
i,e KE = 1/2*m*v2 + 1/2*I*ω2 where I is the moment of inertia of the bowling ball about it's center and ω is the angular velocity
Now for pure rotation (without slipping) v = rω
also for the ball (solid sphere) I = 2/5*m*r2
Hence our kinetic energy becomes
KE = 1/2*m*v2 + 1/5*m*v2 = 7/10*m*v2
so KE = 0.7*7.3*(3.1)2 = 49.10 J = 49 J
Learn more about kinetic energy here
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