Calculus Problem motion along an inclined plane

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dummy123

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Nov 26, 2019
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Hello,

The question is this:
"Suppose that an object starts from rest and slides down a hill whose inclination is 15 degrees. The object slides from a height of 100 feet above the horizontal ground to the ground. How long does it take to slide down the hill and what velocity does the object acquire?"

The answer they gave is approximately 10 seconds; 80 ft/sec.

The equations they give are
a=32 sin A
v= 32t sin A
s=16t^2 sin A

My answer is 4.9=t and v=40.6.

What am I doing wrong?
 
dummy123 said:
Hello,

The question is this:
"Suppose that an object starts from rest and slides down a hill whose inclination is 15 degrees. The object slides from a height of 100 feet above the horizontal ground to the ground. How long does it take to slide down the hill and what velocity does the object acquire?"

The answer they gave is approximately 10 seconds; 80 ft/sec.

The equations they give are
a=32 sin A
v= 32t sin A
s=16t^2 sin A

My answer is 4.9=t and v=40.6.

What am I doing wrong?
Click to expand...
If you want us to catch your mistake - you'll need to share your work in detail.

Please show us how did you arrive at those answers (which equation/s did you use?)
 
Subhotosh Khan said:
Please show us how did you arrive at those answers (which equation/s did you use?)
Click to expand...
Okay.

Because the distance they gave is 100 ft, I did
100 = 16t^2sin15.
Then I rearranged the equation so that it was

sqrt(100 / (16sin15))
=4.9 approximately = t

Then I used
v=32*4.9 sin 15
v=40.6 ft/s
 
Last edited:
dummy123 said:
Okay.

Because the distance they gave is 100 ft, I did
100 = 16t^2sin15.
Then I rearranged the equation so that it was

sqrt(100 / (16sin15))
=4.9 approximately = t

Then I used
v=32*4.9 sin 15
v=40.6 ft/s
Click to expand...
For this problem:

s = 100/sin(15) = 386.37
100 was the vertical distance travelled - NOT total distance travelled (=s).
 
OHHHH.... okay! I got it now.
I didn't make a triangle. I *did* think the total distance travelled was given by 100 ft.

the hypotenuse is 386.37.
therefore, the sqrt(386.37 / (16sin30)) = t
t= 9.66
v=32t * 9.66 sin 15
= 80.

Thank you.
 
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