A new event has been proposed for the Winter Olympics. An athlete will sprint 10

Question

A new event has been proposed for the Winter Olympics. An athlete will sprint 100 m, starting from rest, then leap onto a 22kg bobsled. The person and bobsled will then slide down a 46-m-long ice-covered ramp, sloped at 20?, and into a spring with a carefully calibrated spring constant of 2500N/m . The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 45kg , has been training for this event. She can reach a maximum speed of 15m/s in the 100 m dash. (Figure 1)
How far will Lisa compress the spring?
A new event has been proposed for the Winter Olympics. An athlete will sprint 100 m, starting from rest, then leap onto a 22kg bobsled. The person and bobsled will then slide down a 46-m-long ice-covered ramp, sloped at 20?, and into a spring with a carefully calibrated spring constant of 2500N/m . The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 45kg , has been training for this event. She can reach a maximum speed of 15m/s in the 100 m dash. (Figure 1)
How far will Lisa compress the spring?

Explanation / Answer

first conservation of momentum

45*15 = (45+22)*v

v=10.075 m/s

now conservation of energy

1/2 mv^2 + mg h = 1/2 kx^2

0.5*(45+22)*10.075^2 + (45+22)*9.81*46*sin(20 degrees) = 0.5*2500*x^2

x=3.32 m

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