Question

1. A boat going 10 m/s relative to the water crosses a river flowing 2 m/s downstream. The river is 600 m wide. How long does it take to cross the river? How far downstream does it go?

2. A soccer ball is kicked 25 m/s at an angle of 20 degrees with the ground. How much time is it in the air? How far does it go? Assume it lands at the same level from which it was kicked.

Answer 1

The boat takes approximately 5.77 seconds to cross the river and goes approximately 11.54 meters downstream.

Step-by-step explanation:

To determine the time it takes to cross the river, we need to break down the velocity of the boat into its components. The boat's velocity relative to the water is 10 m/s, and the river's velocity is 2 m/s downstream. Using the Pythagorean theorem, we can find the resultant velocity of the boat, which is /10^2 + 2^2 = /104 m/s. The time it takes to cross the river can be calculated by dividing the width of the river by the resultant velocity, so 600 m / /104 m/s = 5.77 seconds, rounded to two decimal places.

To determine how far downstream the boat goes, we can use the time it takes to cross the river and the river's velocity. The distance is calculated by multiplying the time by the river's velocity, so 5.77 s × 2 m/s = 11.54 m, rounded to two decimal places.

Therefore, it takes approximately 5.77 s to cross the river, and the boat goes approximately 11.54 m downstream.

Learn more about River crossing