The velocity of the ball when it strikes the bottom of the lake is 7.87 m/s.
How to calculate the velocity of the ball?
The velocity of the ball when it strikes the bottom of the lake is calculated by applying the following formula.
v² = u² + 2ah
where;
- v is the final velocity of the ball
- u is the initial velocity of the ball
- a is the acceleration of the ball
- h is the height of fall of the ball
when the ball hits the bottom of the lake, the final velocity will be zero, v = 0
0 = u² + 2ah
0 = 8² + 2(3 - 0.1v²) x 10
0 = 64 + 20(3 - 0.1v²)
0 = 64 + 60 - 2v²
0 = 124 - 2v²
2v² = 124
v² = 124 / 2
v² = 62
v = √62
v = 7.87 m/s
The complete question is below:
A bowling ball is dropped from a boat so that it strikes the surface of a lake with a speed of 8m/s. Assuming the ball experiences a downward acceleration of a=3-0.1v² when in the water determine the velocity of the ball when it strikes the bottom of the lake. (a and v expressed in m/s² and m/s respectively), (height of fall of the ball, h = 10 m)