Question

You stand on a bridge and drop a teddy bear. The teddy bear hits the water below the bridge in 3.5 seconds. One second after dropping the teddy bear, you decide to toss your rubber ducky down as well. How fast would you have to throw the rubber ducky so it hits the water at the same time?

Answer 1

To ensure the rubber ducky hits the water at the same time as a teddy bear that falls for 3.5 seconds, you must throw it at an initial velocity of 24.5 m/s after one second has elapsed.

Step-by-step explanation:

To find out how fast you would have to throw the rubber ducky so that it hits the water at the same time as the teddy bear, we must first recognize that the rubber ducky has one second less of fall time than the teddy bear.

The teddy bear takes 3.5 seconds to hit the water, so the rubber ducky only has 2.5 seconds to reach the water.

Using the equation of motion v = at, where a is the acceleration due to gravity (9.80 m/s2) and t is the time, we can solve for the initial velocity v required for the rubber ducky.

Since the teddy bear is dropped and the rubber ducky is thrown after one second, we have for the rubber ducky: v = at = (9.80 m/s2)(2.5 s).

Hence, the initial velocity with which you must throw the rubber ducky is 24.5 m/s (rounded to the nearest tenth of a meter per second).