The picture below shows a block of mass 5.22kg held against a spring of spring c

Question

The picture below shows a block of mass 5.22kg held against a spring of spring constant k compressed by a distance d = 28.3cm on a frictionless ramp of length L. The ramp has an angle of 20?. A distance x = 1.16m separates the ramp from a landing area that is at the same height as the top of the ramp.(Figure 1)

A: If the mass leaves the end of the spring at a speed of 4.43m/s , what is the spring constant of the spring?

B: If the mass reaches the top of the ramp moving at speed 2.81m/s , what is the length of the ramp?

Measure the length of the ramp from the starting point (compressed spring) as shown in the picture.

C: Does the mass successfully jump the gap and land on the other side?

Explanation / Answer

1) 0.5*k*d^2 = 0.5*m*v^2 + m*g*0.283*sin(20)

k = 1360 N/m


2)

m*g*h = 0.5*m*(v1^2-v2^2)

h = 0.5*(v1^2-v2^2)/g = 0.6 m

L = h/sin(20) = 1.75 m

3)

horizonatl range R = v2^2*sin(2*20)/g = 0.52 m

but the separation is given x = 1.16 m

x>R. so it does not reach the other end

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