Use the figure to the right to answer the next problem. An object of mass m = 100 g slides down without rolling a rough incline from a height H = 60 cm.At
h = 30 cm,the object flies off the incline.The coefficient of kinetic friction is 0.4,and the angle = 30 
-What is the speed of the object just after it leaves the ramp?
A)2.40 m/s
B)1.34 m/s
C)0.77 m/s
D)0.54 m/s
E)None of these is correct.

Question

Use the figure to the right to answer the next problem. An object of mass m = 100 g slides down without rolling a rough incline from a height H = 60 cm.At
h = 30 cm,the object flies off the incline.The coefficient of kinetic friction is 0.4,and the angle = 30 
-What is the speed of the object just after it leaves the ramp?
A)2.40 m/s 
B)1.34 m/s 
C)0.77 m/s 
D)0.54 m/s 
E)None of these is correct.

Quizplus · Accepted Answer

First, we need to find the acceleration of the object down the incline. We can use the formula:
a = gsinθ - μgcosθ
where g is the acceleration due to gravity (9.8 m/s^2), θ is the angle of the incline (30 degrees), and μ is the coefficient of kinetic friction (0.4).
a = (9.8 m/s^2)(sin30°) - (0.4)(9.8 m/s^2)(cos30°) 
a = 2.94 m/s^2
Next, we can use conservation of energy to find the speed of the object just after it leaves the ramp. At the top of the ramp, the total energy is purely potential energy (mgh). At the bottom of the ramp, the total energy is kinetic energy (1/2mv^2) and potential energy (mgh). Since no energy is lost to friction, we can set the two equal to each other:
mgh = 1/2mv^2 + mgh 
Canceling out the mgh terms and solving for v, we get:
v = sqrt(2gh) 
v = sqrt(2(0.3 m)(9.8 m/s^2)) 
v = 1.34 m/s 
Therefore, the answer is B.

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