Answer to Question #147125 in Mechanics | Relativity for Muqeet

Question

Problem Statement

A sports car needs to make a record jump from certain ramp with some specific height covering certain horizontal distance.

Deliverables

Plan & Structure the suitable track while deciding the track height, track helical ramp geometry (for rigid body base analysis only), minimum initial speed, road grip, weight distribution (for rigid body base analysis only), landing safety etc. Justify your results.

Constraints

The car needs to jump through horizontal distance of at least 20 Cars with some suitable height. The Car driver wishes to take the complete one role manoeuvre i.e. rotation along the motion of axis, into the air so that manoeuvre be completed successfully (for rigid body-based analysis condition).

Answer 1

$using\space conservation\space of enery \space when\space v_{1} =0\\ \frac{1}{2} mv^{2}_{1}+(m\times g\times y)=\frac{1}{2} mv^{2}+(m\times g\times \varDelta y ) \\ \frac{1}{2} mv^{2}_{1}+(m\times g\times(y-\varDelta y))=\frac{1}{2} mv^{2} \\ mv^{2}_{1}+2(m\times g\times(y-\varDelta y))=mv^{2}\\ v=\sqrt{v^{2}_{1}+2g(y-\varDelta y))}\\ using\space conservation\space of enery \space when\space v_{2} =0\\ \frac{1}{2} mv^{2}+(m\times g\times\varDelta y _2)=\frac{1}{2} mv^{2}_{2}+m\times g\times H_max \\ mg\varDelta y _2+(\frac{1}{2} mv^{2}_{1}+mg(y-\varDelta y_2)cos\theta=mgH_max\\ H_max=cos\theta(\frac{v_2^{2}}{2g}+((y-\varDelta y_2)+\varDelta y_2\\ H_max=\varDelta y_2+[\frac{v_2^{2}}{2g}+(y-\varDelta y_2)]cos\theta$