If a force does not act parallel to the resulting displacement, what is the effect on the work done by the force?

Answers

Answer 1

Answer: Then only the component of the force that's parallel to the displacement
is used to calculate the work. The component of force that's perpendicular
to the displacement doesn't move through any distance at all, so its contribution
to the total work is zero.

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A rocket travels vertically at a speed of 1300 km/hr.1300 km/hr. The rocket is tracked through a telescope by an observer located 13 km13 km from the launching pad. Find the rate at which the angle between the telescope and the ground is increasing 3 min3 min after the lift-off.

Answers

Final answer:

This calculus problem can be solved by defining the appropriate variables, constructing a relationship using trigonometry, taking the derivative of both sides with respect to time, and solving for the rate of change of the angle with respect to time. The initial distances, rocket's speed, and angle are used to determine the rocket's position after 3 minutes and thus the rate at which the angle is changing.

Explanation:

This problem involves the concept of related rates in calculus and the understanding of trigonometric relationships. Let's denote the rocket's altitude as y and the angle between the ground and the telescope as θ. We know Δy/Δt = 1300 km/hr, we're given the initial distance (13 km), and we want to find Δθ/Δt at 3 min after lift-off.

From trigonometry, we know that tan(θ) = y/x, where x is the horizontal distance (which remains constant at 13 km) and y is the vertical distance (which is changing). Differentiating both sides with respect to t gives sec²(θ) * Δθ/Δt = Δy/Δt / x. Assuming that the speed of the rocket remains constant, we find that y = (1300 km/hr * 3min)*(1hr/60min) = 65 km at 3 min after launch. Plugging x = 13 km and y = 65 km into the equation tan(θ) = y/x, we get θ = atan(65/13) = 78.69°. Now we can solve for Δθ/Δt using the differentiated equation: Δθ/Δt = ( Δy/Δt / x ) / sec²(θ) = (1300 km/hr / 13 km) / sec²(78.69°). Solving this gives the rate of change of θ with respect to time.

Learn more about Related Rates here:

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A spider is crawling on a wall. First it crawls 1 meter up, then 1 meter to the left, and then 1 meter down. what is its total displacement

Answers

1 meter up, 1 meter to the left and then 1 metter down.
It goes 1 meter up and 1 meter down, so its in the same place. The only displacement is 1 meter to the left.

Look at picture:

(hope this helps)

1 meter up and then 1 meter left, and then 1 meter down. The total displacement would be 1 meter. See Ayah's pic to help you understand more better:)

Which one is an accurate description of the process of erosion? A.

breaking rocks into smaller pieces

B.

forming rocks and depositing them in new places

C.

moving bits of rock and soil across the earth’s surface by water, wind, or glaciers

D.

water moving over the earth's surface and into the atmosphere

Answers

The accurate description of the process of erosion is when moving bits of rock and soil across the earth’s surface by water, wind, or glaciers. The answer is letter C.

An accurate description of erosion would be C. moving bits of rock and soil across the earth's surface by water, wind, or glaciers.

Erosion occurs over time when the Earth's surface begins to get worn down resulting in things like valleys, mud after a rainstorm, and rocks located on the bottom of a body of water.

Due to the force of gravity water easily flows from one place to another, which is why erosion occurs.

Where is the error in this sentence ? A great place to visit on a sunny afternoon is Golden Gate park in San Francisco.

Answers

Golden Gate Park is a proper noun, so Park should be capitalized in this sentence.

The correct sentence would be

A great place to visit on a sunny afternoon is Golden Gate Park in San Francisco.

What is the kinetic energy of a 108 kg object that is moving with a speed of 11.1 m/s ?