Question

Would it be possible to direct the speeds that a coaster will reach before its ever placed on a track?How?

Answer 1

Yes, it is possible to determine the final speed of the rollercoaster if the initial speed and the height to be reached are known.

According the principle of conservation of energy, the total kinetic energy is equal to the total potential energy.

$P.E _i + K.E_i = P.E_f + K.E_f \\\\mgh_i + \frac{1}{2} mv_i^2 = mgh_f + \frac{1}{2} mv_f^2\\\\gh_i + \frac{1}{2} v_i^2 = gh_f + \frac{1}{2} v_f^2\\\\g(0) + \frac{1}{2} v_i^2 = gh_f + \frac{1}{2} v_f^2\\\\\frac{1}{2} v_i^2 = gh_f + \frac{1}{2} v_f^2\\\\v_i^2 = 2gh_f + v_f^2\\\\v_i^2 - 2gh_f = v_f^2\\\\v_f = \sqrt{v_i^2 - 2gh_f}$

where;

• $v_i$ is the initial velocity of the roller coaster
• $v_f$ is the final velocity of the roller coaster
• $h_f$ is maximum height reached by the roller coaster

Thus, it is possible to determine the final speed of the rollercoaster if the initial speed and the height to be reached are known.

Learn more about conservation of energy here: brainly.com/question/166559