Question

Salmon often jump waterfalls to reach their breeding grounds.

Starting downstream, 2.72 m away from a waterfall 0.465 m in height, at what minimum speed must a salmon jumping at an angle of 35.8◦ leave the water to continue upstream? The acceleration due to gravity is 9.81 m/s2 .
Answer in units of m/s.

Answer 1

6.07 m/s

Step-by-step explanation:

Given in the x direction:

s = 2.72 m

u = U cos 35.8° m/s

a = 0 m/s²

s = ut + ½ at²

2.72 = (U cos 35.8°) t + ½ (0) t²

2.72 = (U cos 35.8°) t

t = 2.72 / (U cos 35.8°)

Given in the y direction:

s = 0.465 m

u = U sin 35.8° m/s

a = -9.81 m/s²

s = ut + ½ at²

0.465 = (U sin 35.8°) t + ½ (-9.81) t²

0.465 = (U sin 35.8°) t − 4.905t²

Substitute:

0.465 = (U sin 35.8°) [2.72 / (U cos 35.8°)] − 4.905 [2.72 / (U cos 35.8°)]²

0.465 = 2.72 tan 35.8° − 36.29 / (U cos 35.8°)²

36.29 / (U cos 35.8°)² = 1.497

(U cos 35.8°)² = 24.25

U cos 35.8° = 4.924

U = 6.07 m/s