Question

Splash Mountain is one of the steepest water plume rides in the United States. Occupants of the boat fall from a height of 30 m down a wet ramp which makes a 45 degree angle with the horizontal. The mass of the boat and its occupants is 1500 kg. †= 0.10. Determine the final velocity of the boat at the bottom of the incline.

Answer 1

Applying Newton’s 2^nd law in y direction,

Fnet = ma

F_n – mgcosθ = 0

F_n = mgcosθ---------------(1)

F_k = µ_k*F_n -----------------(2)

Applying Newton’s 2^nd law in x direction,

Fnet = ma

F_k - mgsinθ = ma ------------(3)

Adding (1), (2) & (3)

µ_k*mgcosθ - mgsinθ = ma

a = µ_k*gcosθ - gsinθ

a = 0.10*9.8cos45 – 9.8sin45

a = -6.24 m/s²

v_i = 0 m/s, a = -6.24 m/s², d = 30 m , L = d/sin45 = 30/sin45 = 42.43m

v_f² = v_i² +2ad

v_f² = 0^2 +2*-6.24*-42.43

v_f = - 23.01 m/s….negative sign for downward direction