Question

Salmon often jump waterfalls to reach their breeding grounds. Starting downstream, 3.33 m away from a waterfall 0.287 m in height, at what minimum speed must a salmon jumping at an angle of 25.2° leave the water to continue upstream? The acceleration due to gravity is 9.81 m/s².

a) 2.27 m/s
b) 3.79 m/s
c) 6.45 m/s
d) 7.91 m/s

Answer 1

To determine the minimum speed at which a salmon must jump at a 25.2° angle to reach the top of a 0.287 m high waterfall from a distance of 3.33 m, projectile motion formulas are used, leading to the result of 3.79 m/s.

Step-by-step explanation:

The question relates to the projectile motion of a salmon attempting to jump over a waterfall to reach its breeding grounds. To solve this, we must consider the vertical and horizontal components of the motion separately. Notably, we are looking for the initial speed that allows the salmon to clear the vertical height of the waterfall.First, resolve the gravitational acceleration component (9.81 m/s²) to calculate the time needed for the salmon to reach the maximum height of 0.287 m. Then, determine the horizontal velocity that would allow the salmon to cover the 3.33 m distance to the waterfall in the same amount of time.Using kinematic equations for projectile motion and the given angle of 25.2°, the minimum speed required can be found. The correct choice that satisfies both the horizontal distance and vertical height requirements is option (b) 3.79 m/s.