A 1052 kg boulder slides down a sloping hillside during a landslide. The hillside slopes at an angle of 3 degrees to the horizontal, and the frictional forces on the boulder add up to 205 newton.What is the boulder's acceleration down the slope? Give your answer to one decimal place.

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BlackTom AI · Accepted Answer

The problem asks for the acceleration of a boulder sliding down a slope with given mass, slope angle, and total frictional force. 
First, identify the forces along the slope: gravity components along the slope provide driving force, while friction resists motion. 
The downslope component of gravity is m g sin(theta). With m = 1052 kg, g ≈ 9.8 m/s^2, and theta = 3 degrees, sin(3°) ≈ 0.052336, so m g sin(theta) ≈ 1052 × 9.8 × 0.052336 ≈ 1052 × 0.5128 ≈ 539.5 N (but we will focus on the net acceleration per unit mass below). 
The total frictional force opposing motion is F_f = 205 N. 
Net force along the slope is F_net = m g sin(theta) − F_f. 
To find acceleration, a = F_net / m = g sin(theta) − (F_f / m). 
Compute the terms: g sin(theta) ≈ 9.8 × 0.052336 ≈ 0.5128 m/s^2, and F_f / m = 205 / 1052 ≈ 0.1948 m/s^2. 
Subtracting yields a ≈ 0.5128 − 0.1948 ≈ 0.3180 m/s^2. 
Rounding to one decimal place gives a ≈ 0.3 m/s^2. 
Thus, the boulder accelerates downslope at about 0.3 m/s^2. 
Note on inputs: since no multiple-choice options were provided, this analysis used the standard physics model for motion on an incline with kinetic friction, and the result aligns with the given numerical answer format.

A 1052 kg boulder slides down a sloping hillside during a landslide. The hillside slopes at an angle of 3 degrees to the horizontal, and the frictional forces on the boulder add up to 205 newton.What is the boulder's acceleration down the slope? Give your answer to one decimal place.

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