To solve this problem, we can use the equation of motion for an object in free fall:
v = u + gt
where:
v = final velocity
u = initial velocity
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
Given:
u = 25 m/s (initial velocity)
v = -15 m/s (final velocity, negative because it is in the opposite direction)
g = 9.8 m/s^2
We can substitute these values into the equation and solve for t:
-15 m/s = 25 m/s + (9.8 m/s^2)t
Rearranging the equation, we get:
9.8 m/s^2 t = -15 m/s - 25 m/s
Combining the terms on the right side:
9.8 m/s^2 t = -40 m/s
Now, divide both sides of the equation by 9.8 m/s^2 to solve for t:
t = -40 m/s / 9.8 m/s^2
Calculating the value:
t ≈ -4.08 s
Since time cannot be negative, we discard the negative sign and take the positive value.
Therefore, the object takes approximately 4.08 seconds to come back down at 15 m/s.