Question

An arrow is launched straight up with a velocity of 12.6 m per second. How long before the arrow returns to the ground?

a) 2.55 seconds
b) 5.1 seconds
c) 7.65 seconds
d) 12.6 seconds

Answer 1

The arrow takes approximately 2.58 seconds to return to the ground.

Step-by-step explanation:

First, we need to determine the time it takes for the arrow to reach its maximum height. Since the arrow is launched straight up, it will reach its maximum height when its vertical velocity becomes zero. We can use the formula: final velocity = initial velocity + acceleration*time.

Given that the initial velocity is 12.6 m/s, the final velocity should be 0 m/s, and the acceleration due to gravity is -9.8 m/s² (taking downwards as the positive direction), we can solve for time:

0 = 12.6 - 9.8*time

9.8*time = 12.6

time = 12.6/9.8 = 1.29 seconds (approximately, rounded to two decimal places).

Next, we know that it takes the same amount of time for the arrow to go up as it does to come back down. Therefore, the total time before the arrow returns to the ground is twice the time it takes to reach its maximum height:

Total time = 2 * 1.29 = 2.58 seconds (approximately).