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leoflindall
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Homework Statement
I have solved the following question in two ways which give different answers. Both methods are similar but a little bit different so I think one is wrong. Can anyone advise me which (if either) of the answers is right?
A stuntman is preparing his next stunt. He needs to get his car airborne once he reaches the top of the hill. The hilltop is roughly a vertical circle with radius 100m. How fast does he need to drive.
Homework Equations
E=1/2 m v^2
PE=mgh
Centripetal acceleration (a) = (V^2)/r
The Attempt at a Solution
Solution 1.
At the point of takeoff the energy of the car must be equal to the potential energy at the top oh the hill. So we can say that KE=PE, and thus
1/2 mv^2 = mgh
which rearranged:
V = [tex]\sqrt{2 g r}[/tex] , where r is the radius of the hill, and g is the acceleration.
This gives an answer of 99.6 mpm.
Solution 2
At the point of take off the Force acting upwards on the car must be equal to the weight (mg) of the car. Knowing the formula for centripetal acceleration we can derive an equation for the force upwards,
F = m [tex]\frac{V^{2}}{r}[/tex]
This equated to mg yields,
mg=m[tex]\frac{V^{2}}{r}[/tex]
which rearranges;
V =[tex]\sqrt{gr}[/tex]
which gives an answer of 70.4mph.
Both answers are plausible as there is only a factor of root 2 difference. I would be very appreciative if anyone could advise me as to which method is correct, and what is wrong with the other!
Leo