A mouse runs along a baseboard in your house. The mouse's position as a function of time is given by x(t)=pt2+qt, with p = 0.36

Answer:

11.56066 m/s

Explanation:

m = Mass of individual

v = Velocity of individual = 13.4 m/s

g = Gravitational acceleration = 9.81 m/s²

v' = Velocity of the individual after dropping

At the surface, kinetic and potential energy will equalize

The cliff's height is 9.15188 m

Define fall height as h' = 2.34 m

The person's speed is 11.56066 m/s

Answer:

3.4 x 10⁴ m/s

Explanation:

Analyze the circular path of the electron

B = magnetic field = 80 x 10⁻⁶ T

m = mass of an electron = 9.1 x 10⁻³¹ kg

v  = speed in the radial direction

r = radius of the circular trajectory = 2 mm = 0.002 m

q = charge of an electron = 1.6 x 10⁻¹⁹ C

For the electron’s circular movement

qBr = mv

(1.6 x 10⁻¹⁹) (80 x 10⁻⁶) (0.002) = (9.1 x 10⁻³¹) v

v = 2.8 x 10⁴ m/s

Now, consider the electron's movement in a straight line:

v' = speed in linear motion

x = distance traveled horizontally = 9 mm = 0.009 m

t = duration = = = 4.5 x 10⁻⁷ sec

Using the formula

x = v' t

0.009 = v' (4.5 x 10⁻⁷)

v' = 20000 m/s

v' = 2 x 10⁴ m/s

The resultant speed is given by

V = sqrt(v² + v'²)

V = sqrt((2.8 x 10⁴)² + (2 x 10⁴)²)

v = 3.4 x 10⁴ m/s

1. τbiceps = +(Positive) 2. τforearm = -(Negative) 3. τball = -(Negative) Explanation: The attached figure illustrates the following: 1. For the biceps, τbiceps indicates that torque is calculated as Torque = r x F, where r and F are vectors. Here, r corresponds to the vector from the elbow to the biceps. In the figure, the force from the biceps is directed upwards. Applying the right-hand rule from r to F results in counterclockwise torque, which is considered positive (+). 2. The torque related to the weight of the forearm, τforearm, uses the same torque formula, with r being the vector from the elbow to the forearm. The weight acts downward, causing a clockwise torque that is negative (-). 3. Similarly, for the weight of the ball, τball, the downward force from the ball's weight generates a clockwise torque, which also registers as negative (-).