Question

A roller coaster is travelling without friction as

shown in the diagram. If the speed of the roller
coaster at A is 3.0 m/s, what is the speed at B?

Answer 1

Thus, the speed at B = 13 m/s

Step-by-step explanation:

From the attached image:

Using the conservation of energy;

Iinital M.E = Final M.E

where;

M.E = mechanical energy

∴

`(1)/(2) * m * v_A^2+ mgh_A = (1)/(2) * m * v_B^2+ mgh_B`

`(1)/(2) * m * 3^2+m * 9.8 * 15 = (1)/(2) * m * v_B^2+ m* 9.8 * 7 \\ \\ (1)/(2) * 3^2 + 9.8 * 15 = (1)/(2) * v^2 + 9.8 * 7 \\ \\ \implies 151.5 = 0.5 v^2 + 68.6 \\ \\ 0.5v^2 = 151.5 - 68.6 \\ \\ 0.5 v^2 = 82.9 \\ \\ v^2 = (82.9)/(0.5) \\ \\ v^2 = 165.8 \\ \\ v = √(165.8) \\ \\ v = 12.9 \ m/s\\ \\ \mathbf{v \simeq 13 \ m/s}`