Physics, 03.08.2019 04:30 phillipfruge3

Achevrolet corvette convertible can brake to a stop from a speed of 60.0 mi/h in a distance of 123 ft on a level roadway. what is its stopping distance on a roadway sloping downward at an angle of 17.0°?

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Answer from: germainenez8403

The stopping distance of the car when the road slopes at 17⁰ is 128.7 ft.

The given parameters;

speed of the car, v = 60 mi/h

distance traveled on a level roadway = 123 ft

the sloping angle of the new road, Ф = 17⁰

A simple sketch of the problem is given below;

start-------------123ft--------------------end

17⁰ ↓

↓

↓new end due to the given slope

A straight line joining the start and the new end point forms a hypotenuse of the triangle and it will be equal to the new stopping distance of the car.

Apply trigonometry ratio concept to determine the new stopping distance;

$cos (\theta ) = \frac{adjacent}{hypotenuse} \\\\cos(17) = \frac{123 \ ft}{new \ stopping \ distance} \\\\new \ stopping \ distance = \frac{123 \ ft}{cos(17)} \\\\new \ stopping \ distance = \frac{123 \ ft}{0.956} \\\\new \ stopping \ distance = 128.7 \ ft$

Thus, the stopping distance of the car when the road slopes at 17⁰ is 128.7 ft.

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Answer from: williamlindley2

By definition we have that the final speed is:
Vf² = Vo² + 2 * a * d
Where,
Vo: Final speed
a: acceleration
d: distance.
We cleared this expression the acceleration:
a = (Vf²-Vo²) / (2 * d)
Substituting the values:
a = ((0) ^ 2- (60) ^ 2) / ((2) * (123) * (1/5280))
a = -77268 mi / h ^ 2
its stopping distance on a roadway sloping downward at an angle of 17.0 ° is:
First you must make a free body diagram and see the acceleration of the car:
g = 32.2 feet / sec ^ 2
a = -77268 (mi / h ^ 2) * (5280/1) (feet / mi) * (1/3600) ^ 2 (h / s) ^ 2
a = -31.48 feet / sec ^ 2
A = a + g * sin (θ) = -31.48 + 32.2 * sin17.0
A = -22.07 feet / sec ^ 2
Clearing the braking distance:
Vf² = Vo² + 2 * a * d
d = (Vf²-Vo²) / (2 * a)
Substituting the values:
d = ((0) ^ 2- (60 * (5280/3600)) ^ 2) / (2 * (- 22.07))
d = 175.44 feet

its stopping distance on a roadway sloping downward at an angle of 17.0 ° is 175.44 feet

Answer from: Quest

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Answer from: Quest

m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| = √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| = √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| = 14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s

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