Question

A worker painting a bridge drops his paintbrush. When the paintbrush hits the water, it is moving at 15.8 m/s. How high above the water was the worker when he dropped the paintbrush?

Answer 1

Using the kinematic equation for an object in free fall and given a final velocity of 15.8 m/s when the paintbrush hits the water, we calculate that the worker was 12.7 meters above the water when he dropped the paintbrush.

Step-by-step explanation:

To calculate the height from which the worker dropped his paintbrush, we can use the kinematic equations for an object in free fall. Since the problem states to ignore air resistance, we can assume the only force acting on the paintbrush while falling is gravity. The final velocity (v) of the paintbrush when it hits the water is given as 15.8 m/s. The acceleration (a) due to gravity is 9.8 m/s2, which is constant, and since the paintbrush was dropped (not thrown), the initial velocity (u) is 0 m/s. We can use the following kinematic equation to solve for the height (h):

v2 = u2 + 2ah

Substituting the known values:

15.8 m/s2 = 0 + 2(9.8 m/s2)h

Solving for h:

15.8 m/s2 = 19.6 m/s2h

h = (15.8 m/s)2 / (19.6 m/s2)

h = 12.7 m

Therefore, the worker was 12.7 meters above the water when he dropped his paintbrush.