Trying to escape his pursuers, a secret agent skis off a
slope inclined at 30° below the horizontal at 60 km/h. To
survive and land on the snow 100 m below, he must clear a
gorge 60 m wide. Does he make it? Ignore air resistance.
1 answer
Yes, he makes it. The horizontal distance he needs to travel is 100 m, and the horizontal velocity he has is 60 km/h, which is equal to 16.67 m/s. Therefore, the time it takes him to travel the 100 m is 100/16.67 = 6 seconds. The vertical distance he needs to travel is 60 m, and the vertical velocity he has is equal to the component of his velocity that is perpendicular to the slope, which is equal to 50 km/h, or 13.89 m/s. Therefore, the time it takes him to travel the 60 m is 60/13.89 = 4.33 seconds. Since 4.33 seconds is less than 6 seconds, he will make it.
0 answers