f a car is speeding down a road at 40 miles/hour (mph), how long is the stopping distance D40 compared to the stopping distance

Answer:

2.5 m

Explanation:

Billboard worker's weight = 800 N

Number of ropes = 2

Length of scaffold = 4 m

Weight of scaffold = 500 N

Tension present in rope = 550 N

The total torques will be

The worker is positioned at 2.5 m

Answer:

v = [√(g/2h)]L

Explanation:

Let v represent the initial horizontal speed, and t denote the duration James Bond takes to leap off the ledge of length, L.

Thus, we derive vt = L, which leads to t = L/v

Additionally, considering that Bond begins with no horizontal velocity, he descends freely over the height, h; thus the equation y - y' = ut - 1/2gt² is applicable, where y = 0 (top of the cliff) and y' = -h, u = 0 (initial vertical speed), g = acceleration due to gravity = 9.8 m/s², and t = the time required to leap from the cliff = L/v.

By substituting these parameters into the equation, we obtain

y' - y = ut - 1/2gt²

-h - 0 = 0 × t - 1/2g(L/v)²

-h  = - 1/2gL²/v²

v² = gL²/2h

taking the square root of both sides gives us

v = [√(g/2h)]L

Therefore, James Bond's required minimum horizontal velocity is v = [√(g/2h)]L

Answer:

The current flowing through the tube is 0.601 A

Explanation:

Given data;

the diameter of the fluorescent tube is d = 3 cm

the incoming negative charge in the tube is -e = 3 x 10¹⁸ electrons/second

the outgoing positive charge equals +e = 0.75 x 10¹⁸ electrons/ second

The current within the fluorescent tube results from both positive and negative charges which contribute to maintaining electrical neutrality in the conductor (fluorescent tube).

Q = It

I = Q/t

where;

I signifies current in Amperes (A)

Q represents charge measured in Coulombs (C)

t denotes time which is in seconds (s)

1 electron (e) accounts for 1.602 x 10⁻¹⁹ C

Thus, 3 x 10¹⁸ e/s can be computed as

= (3 x 10¹⁸ e/s  x 1.602 x 10⁻¹⁹ C) / 1e

= 0.4806 C/s

This reflects the negative charge per second (Q/t) = 0.4806 C/s

Meanwhile, the positive charge per second amounts to

(0.75 x 10¹⁸ e/s  x 1.602 x 10⁻¹⁹ C) / 1e

Thus, the positive charge per second is equal to 0.12015 C/s

The total charge per second in the tube is then obtained by summing both charges: Q / t = (0.4806 C/s + 0.12015 C/s)

                                                                I = 0.601 A

Therefore, the current within the tube computes to 0.601 A

Answer:

La magnitud del momento total es de 21.2 kg m/s y su dirección es de 39.5° respecto al eje x.

Explanation:

¡Hola!

El momento total se calcula como la suma de los momentos de las piezas.

El momento de cada pieza se calcula de la siguiente manera:

p = m · v

Donde:

p = momento.

m = masa.

v = velocidad.

El momento es un vector. La pieza de 200 g se mueve a lo largo del eje x, por lo que su momento será:

p = (m · v, 0)

p = (0.200 kg · 82.0 m/s, 0)

p = (16.4 kg m/s, 0)

La pieza de 300 g se mueve a lo largo del eje y. Su vector momento será:

p =(0, m · v)

p = (0, 0.300 kg · 45.0 m/s)

p = (0, 13.5 kg m/s)

El momento total es la suma de cada momento:

Momento total = (16.4 kg m/s, 0) + (0, 13.5 kg m/s)

Momento total = (16.4 kg m/s + 0, 0 + 13.5 kg m/s)

Momento total = (16.4 kg m/s, 13.5 kg m/s)

La magnitud del momento total se calcula de la siguiente manera:

La dirección del vector de momento se calcula utilizando trigonometría:

cos θ = px/p

Donde px es el componente horizontal del momento total y p es la magnitud del momento total.

cos θ = 16.4 kg m/s / 21.2 kg m/s

θ = 39.3 (39.5° si no redondeamos la magnitud del momento total)

The complete question is;

A ski jumper descends a ramp and exits the ski track at a horizontal speed of 24 m/s. The slope at the landing site angles downwards at θ = 59◦. The acceleration due to gravity is 9.8 m/s².

What is the value of the relative angle φ at which the ski jumper makes contact with the slope? Provide the answer in degrees.

Answer:

14.08°

Explanation:

The time taken can be calculated using the formula;

t = (2V_x•tan θ)/g

t = (2 × 24 × tan 59)/9.8

t = 8.152 s

Next, the slope of the trajectory at the impact point is determined by;

tan α = V_y/V_x

Given V_x = 24 m/s

We will find V_y using;

v = gt

Therefore;

V_y = gt

V_y = 9.8 × (8.152) = 78.89 m/s

Thus;

tan α = 78.89/24

tan α = 3.2871

α = tan^(-1) 3.2871

α = 73.08°

Consequently;

Relative angle φ = α - θ = 73.08 - 59 = 14.08°