Answer:
v_y = 12.54 m/s
Explanation:
Given values:
- Initial vertical height y_o = 10 m
- Initial velocity v_y,o = 0 m/s
- The object's acceleration in the air = a_y
- The actual time taken to reach the ground t = 3.2 s
Find:
- How to calculate the object's speed when it arrives at the ground?
Solution:
- Apply kinematic equations to find the actual acceleration of the ball when it reaches the ground:
y = y_o + v_y,o*t + 0.5*a_y*t^2
0 = 10 + 0 + 0.5*a_y*(3.2)^2
a_y = - 20 / (3.2)^2 = 1.953125 m/s^2
- Use the total energy conservation principle of the system:
E_p - W_f = E_k
Where, E_p = m*g*y_o
W_f = m*a_y*(y_i - y_f)..... Reflecting air resistance
E_k = 0.5*m*v_y^2
Thus, m*g*y_o - m*a_y*(y_i - y_f) = 0.5*m*v_y^2
g*(10) - (1.953125)*(10) = 0.5*v_y^2
v_y = sqrt(157.1375)
v_y = 12.54 m/s
a) x_{cm} = m₂/ (m₁ + m₂) d, b) x_{cm} = 52.97 pm
To solve this problem, Coulomb's law will be applied as follows:
F = k*q1*q2 / r^2 where:
F indicates the force magnitude between the charges
k is a constant = 9.00 * 10^9 N.m^2/C^2
q1 = <span>+2.4 × 10–8 C
q2 = </span><span>+1.8 × 10–6 C
r represents the distance separating the charges = </span><span>0.008 m
By substituting these values, we derive:
F = (9*10^9)(2.4*10^-8)(1.8*10^-6) / (0.008)^2 = 6.075, which rounds to 6.1 Newtons
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Answer:
The rotational angular speed is measured at 1.34 rad/s.
Explanation:
Considering the following parameters,
Length = 3.40 m
Distance = 5.90 m
Angle = 45.0°
We are tasked with finding the angular speed of rotation
Using the balance equation
Horizontal component


Vertical component

Substituting the tension value


Substituting the value into the equation


Thus, the angular speed of rotation computes to 1.34 rad/s.
25.82 m/s
Explanation:
Given:
Force applied by the baseball player; F = 100 N
Distance the ball travels; d = 0.5 m
Mass of the ball; m = 0.15 kg
To find the velocity at which the ball is released, we will equate the work done with the kinetic energy involved.
It's important to recognize that work done reflects the energy the baseball player has used. Thus, the relationship can be represented as follows:
F × d = ½mv²
100 × 0.5 = ½ × 0.15 × v²
Solving gives:
v² = (2 × 100 × 0.5) / 0.15
v² = 666.67
v = √666.67
v = 25.82 m/s.