Question

A cart travels along a frictionless roller coaster track. At point A, the cart is 10 m above the ground and traveling at 2 m/s.

a) What is the velocity at point B when the cart reaches the ground? (2 mark)





b) What is the velocity of the cart at point C when the cart reaches a height of 3 m? (2 mark)





c) What is the maximum height the cart can reach before the cart stops?

Answer 1

a)

$$v_b^2=v_a^2+2gH\to v_b^2=2^2+2(9.8)(10)$$

$$v_b=14.1\frac{m}{s}$$

b)

$$v_c^2=v_a^2+2g(H-h)\to v_c^2=2^2+2(9.8)(10-3)$$

$$v_c=11.9\frac{m}{s}$$

c)

$$2gH_m=v_a^2+2gH\to 2^2=2(9.8)(H_m-10)$$

$$H_m=10.2\ m$$