Final answer:
The total time for a ball thrown upward at a speed of 13.7 m/s to return to the starting point can be found by doubling the time it takes to reach the highest point of its trajectory.
Step-by-step explanation:
To determine how long it will take for a ball thrown vertically upward with a given speed to return to its starting point, we can use the equations of motion for an object under the influence of gravity. In this case, the ball is thrown upward with a speed of 13.7 m/s, and we'll use the acceleration due to gravity, which is approximately 9.8 m/s2 downward. The total time for the ball to return will be twice the time it takes to reach the peak of its motion (where its velocity is zero).
The time to reach the peak can be calculated using the formula t = v/g, where v is the initial velocity and g is the acceleration due to gravity. Plugging in the values we have t = 13.7 m/s / 9.8 m/s2, which gives us the time to reach the peak. To find the total time for the round trip, we simply double this time.