Home
Home
Writing Helper
Writing Helper
Calculator
Calculator
Resources
Resources
Blog
Blog
App
App

Chrome Extension

Crop questions and get answers on any web page

Install now
Home
Study Resources
Physics
Questions

Question

If air resistance is negligible, the power required by a car to drive at constant speed up a hill inclined at 30° to the horizontal is P. What power is required by the car to drive at the same constant speed up a hill inclined at 60° to the horizontal? (A) 2P (B) Greater than P but less than 2P (C) P (D) Less than P but greater than P/2 (E) P/2

If air resistance is negligible, the power required by a car to drive at constant speed up a hill inclined at 30° to the horizontal is P. What power is required by the car to drive at the same constant speed up a hill inclined at 60° to the horizontal? (A) 2P (B) Greater than P but less than 2P (C) P (D) Less than P but greater than P/2 (E) P/2

Show transcript
Asked in United States

Gauth AI Solution

Super Gauth AI

93%(592 rated)

Answer

(B) Greater than P but less than 2P

Explanation

When air resistance is negligible, the power required by a car to drive at constant speed up a hill is given by the equation:
P=mgvsin⁡(θ)P = mgv\sin(\theta)
where P is the power, m is the mass of the car, g is the acceleration due to gravity, v is the velocity of the car, and θ is the angle of the hill

We are given that the power required to drive up a hill inclined at 30∘30^{\circ} is P

To find the power required to drive up a hill inclined at 60∘60^{\circ}, we can use the same equation and substitute θ with 60∘60^{\circ}:
P′=mgvsin⁡(60∘)P' = mgv\sin(60^{\circ})
Since sin⁡(60∘)=32\sin(60^{\circ}) = \frac{\sqrt{3}}{2}, we can simplify the equation to:
P′=32mgvP' = \frac{\sqrt{3}}{2}mgv
Comparing P' with P, we can see that P' is greater than P but less than 2P

Therefore, the answer is (B) Greater than P but less than 2P
Helpful
Not Helpful
Super Gauth AI
😉 Want a more accurate answer?
Get step by step solutions within seconds.
Related
Suppose a rescue airplane drops a relief package while it is moving with a constant horizontal speed at an elevated height. Assuming that air resistance is negligible, where will the relief package land relative to the plane? Justify your answer.
98% (228 rated)
A navy cargo plane drops drops bundles of shelters and mosquito nets onto a field in rural Kenya. It is moving with a constant horizontal speed at an elevated height. Assuming that air resistance is negligible, where will the packages land relative to the plane?
80% (2 rated)
An object is thrown with an initial speed u near the surface of Earth. Assume that air resistance is negligible and the gravitational field is constant. If the object is thrown horizontally, the direction and magnitude of its acceleration while it is in the air is
Mark for Review An object is thrown with an initial speed u An object is thrown with an initial speed v near the surface of Earth. Assume that air near the surface of Earth. Assume that air resistance is negligible and the gravitational resistance is negligible and the gravitational field is constant. field is constant If the object is thrown horizontally, the direction and magnitude of its acceleration while it is in the air is A upward and decreasing upward and constant downward and decreasing downward and increasing downward and constant
0 What is the y-intercept?