A new event has been proposed for the Winter Olympics. As seen in the figure bel

Question

A new event has been proposed for the Winter Olympics. As seen in the figure below, an athlete will sprint 100 m, staring from rest, then leap onto a 20 kg bobsled. The person and the bobsled will then slide A down a 50-m-long ice-covered ramp, sloped at 20 degree, and into a spring with a carefully calibrated spring constant of 2000 N/m. The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 40 kg, has been training for this event. She can reach a maximum speed of 12 m/s in the 100 m dash. How far will Lisa compress the spring?

Explanation / Answer

Here ,

theta = 20 degree

distance ,d = 50 m

spring constant , k = 2000 N/m

mass of lisa , m = 40 Kg

Using conservation of energy

0.5 * k * x^2 = m * g * h * sin(theta) + 0.5 * m * v^2

0.5 * 2000 * x^2 = 40 * 9.8 * 50 * sin(20) + 0.5 * 40 * 12^2

solving for x

x = 3.06 m

the distance compressed by lisa is 3.06 m

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