Question

A loaded 400 kg toboggan is traveling on smooth horizontal snow at 4.80 m/s when it suddenly comes to a rough region. The region is 7.00 m long and reduces the toboggan's speed by 1.30 m/s. By what percent did the rough region reduce the toboggan's kinetic energy and speed?

Answer 1

The rough region reduced the toboggan's kinetic energy by 44% and its speed by 73%.

Step-by-step explanation:

To find the percent by which the rough region reduced the toboggan's kinetic energy and speed, we need to compare the kinetic energy before and after the rough region.

The initial kinetic energy of the toboggan can be calculated using the formula: KE = 0.5 * mass * velocity^2. Plugging in the values, KE = 0.5 * 400 kg * (4.80 m/s)^2 = 4608 J.

The final kinetic energy of the toboggan can be calculated using the reduced velocity: KE = 0.5 * 400 kg * (4.80 m/s - 1.30 m/s)^2 = 2576 J.

The percent reduction in kinetic energy is (4608 J - 2576 J) / 4608 J * 100% = 44%. Similarly, the percent reduction in speed is (4.80 m/s - 1.30 m/s) / 4.80 m/s * 100% = 73%.