a rollar coaster is 80m high and has a 50kg car at rest. Ignore air resistance and friction.
If the speed of the car is 60m/s what is the height?
0+50(9.8)(80) = 1/2(50)(vf^2) + (60)^2 + 50(9.8)(h).
Is this equation correct?? If so I do not know how to solve for h since on the right side there is the h and vf^2.
m g * falling distance = (1/2)m (60)^2
m cancels
Find falling distance, subtract from 80
Your equation is right but note that 50 cancels and you really have m g (80-h).
remember that vf = 60 is given
If I wrote all this your way I would have
0 + m g (80) = (1/2)m(60^2) + m g (h)
or
9.8(80-h) = (1/2)(3600)
so on the left side of the equation the mass is gone and on the right side the mass and gravity is gone.
So the anwser would be 784h = 1800
h=2.2
Is that correct?
I did the math wrong, I got 103 now.
If the roller-coaster starts from rest at the hill ita speed at the bottom of the 80- m hill is
m•g•h =m•v²/2,
v=sqrt(2•g•h) = sqrt(2•9.8•80)= 39.6 m/s.
Therefore, I believe that you have the mistake in your given data: the velocity may be
60 km/hr = 16.67 m/s. Then the problem makes sense.
So, if we have to find at what height the car has the velocity “v”,the solution is
mg(H-h) = mv²/2.
h = H - v²/2•g = 80 – (16.67) ²/2•9.8 = 65.8 m
Yes, the equation you wrote is correct. To solve for h, you need to rearrange the equation and isolate the variable h.
Let's break down the equation and rearrange it step by step:
Starting equation:
0 + 50(9.8)(80) = 1/2(50)(vf^2) + (60)^2 + 50(9.8)(h)
First, let's simplify the left side of the equation:
0 + 50(9.8)(80) = 1/2(50)(vf^2) + 3600 + 50(9.8)(h)
Multiplying the values:
0 + 39200 = 25(vf^2) + 3600 + 490h
Next, let's group the terms on the right side of the equation:
39200 - 3600 = 25(vf^2) + 490h
35600 = 25(vf^2) + 490h
Now, let's isolate the term with 'h':
35600 - 25(vf^2) = 490h
Finally, we can solve for 'h' by dividing both sides of the equation by 490:
h = (35600 - 25(vf^2))/490
Plugging in the given value for vf (60 m/s):
h = (35600 - 25(60^2))/490
After evaluating the right side of the equation, you'll get the height 'h' in meters.