A. The horizontal component of velocity is
vx = dx/dt = π - 4πsin(4πt + π/2)
vx = π - 4πsin(0 + π/2)
vx = π - 4π(1)
vx = -3π
b. vy = 4πcos(4πt + π/2)
vy = 0
c. m = sin(4πt + π/2) / [πt + cos(4πt + π/2)]
d. m = sin(4π/6 + π/2) / [π/6 + cos(4π/6 + π/2)]
e. t = -1.0
f. t = -0.35
g. To find t, set
vx = π - 4πsin(4πt + π/2) = 0
Then use this to calculate vxmax
h. To determine t, set
vy = 4πcos(4πt + π/2) = 0
Then use this to find vymax
i. s(t) = [x(t)^2 + y(t)^2]^(1/2)
h. s'(t) = d[x(t)^2 + y(t)^2]^(1/2) / dt
k and l. Determine the values for t
d[x(t)^2 + y(t)^2]^(1/2) / dt = 0
And substitute to find both the maximum and minimum speeds.
Answer
Data provided:
mass of the block = 200 g = 0.2 Kg
Velocity at A = 0 m/s
Velocity at B = 8 m/s
distance of slide = 10 m
height of the block = 4 m
calculation for the block's potential energy
P = m g h
P = 0.2 x 9.8 x 4
P = 7.84 J
kinetic energy calculated as



Work done = P - KE
work = 7.84 - 6.14
work = 1.7 J
b) using the formula v² = u² + 2 a s
0 = 8² - 2 x a x 10
a = 3.2 m/s²
ma - μ mg = 0



Answer: t = 0.878s
Explanation: A note for you,
since the temperature decreases in a straight line, you can expect the movement speed to also behave linearly. However, this isn't exactly true (referring to the formula). Alternatively, utilize the interpolation principle: (x/v_surface + x/v_top)/2 = t.
While the answer may not match exactly, it should be a close approximation. You can use this formula, thus avoiding large distance calculations.
Answer:

Explanation:
The friction created between the tire and the ground generates thermal energy as force is applied during skidding.
The mentioned force relates to half the impact on the rear tire, resulting in a calculated normal force of,

The work executed is determined by the frictional force and the distance covered,

Where ![\mu_k [/ tex] is the coefficient of kinetic frictionN is the normal force previously found d is the distance traveled,Replacing,[tex]W_f = (0.80)(441)(0.42)](https://tex.z-dn.net/?f=%20%5Cmu_k%20%5B%2F%20tex%5D%20is%20the%20coefficient%20of%20kinetic%20friction%3C%2Fp%3E%3Cp%3EN%20is%20the%20normal%20force%20previously%20found%20d%20is%20the%20distance%20traveled%2C%3C%2Fp%3E%3Cp%3EReplacing%2C%3C%2Fp%3E%3Cp%3E%5Btex%5DW_f%20%3D%20%280.80%29%28441%29%280.42%29)
The thermal energy produced from the work done is,

To find the mass using a weight of 1.4 N:
1.4/9.8 = 0.1428 kg
The momentum is calculated as 0.1428 multiplied by 44.7, which is 6.38 kgm/s.