Answer to Question #128584 in Mechanics | Relativity for Amelia

Question #128584
A race car collided with race track wall.Just before the collision,he is travelling at speed v1= 70m/s along a straight line at 30 degrees from the wall. Just after collision he is travelling at speed 50m/s along a straight line at 10 degree from the wall.His mass is 80kg.(a) the impulse J of the driver due to collision
(b)the collision last for 14ms.What is the magnitude of the average force on the driver during collision
Expert's answer

The change of impulse can be calculated as the sum of changes in parallel and perpendicular to the wall directions.

"J_{\\text{par}} = m(v_2\\cos\\alpha_2 - v_1\\cos\\alpha_1) = 80\\,\\mathrm{kg}\\cdot(50\\,\\mathrm{m\/s}\\cdot\\cos10^\\circ - 70\\,\\mathrm{m\/s}\\cdot\\cos30^\\circ ) = -911\\,\\mathrm{kg\\cdot m\/s} \\\\\nJ_{\\text{perp}} = m(v_2\\sin\\alpha_2+ v_1\\sin\\alpha_1) = 80\\,\\mathrm{kg}\\cdot(50\\,\\mathrm{m\/s}\\cdot\\sin10^\\circ+ 70\\,\\mathrm{m\/s}\\cdot\\sin30^\\circ ) =3495\\,\\mathrm{kg\\cdot m\/s}."

(a) The total change of impulse of the driver can be calculated by means of the Pythagorean theorem:

"J = \\sqrt{J_{\\mathrm{par}}^2 + J_{\\mathrm{perp}}^2} = 3611\\,\\mathrm{kg\\cdot m\/s}."

(b) The change of impulse obtained above is due to the force from interaction with the wall. So the average force can be calculated as

"F_{\\text{av}} = \\dfrac{J}{\\Delta t} = \\dfrac{3611\\,\\mathrm{kg\\cdot m\/s}}{0.014\\,\\mathrm{s}} \\approx 2.6\\cdot10^5\\,\\mathrm{N}."

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