When an object is thrown upward, it follows a projectile motion. To determine how long the object will remain in the air, we need to calculate the time of flight.
Given: Initial upward velocity (u) = 15 m/s
In projectile motion, the object reaches its highest point when its vertical velocity becomes zero. We can use this information to find the time it takes for the object to reach its highest point.
Using the equation for vertical motion:
v = u + at
At the highest point, the final vertical velocity (v) is zero, and the acceleration due to gravity (a) is -9.8 m/s² (taking downward as the positive direction).
0 = u + (-9.8) * t_highest
Solving for t_highest:
u = 9.8 * t_highest
t_highest = u / 9.8
t_highest = 15 / 9.8 ≈ 1.53 s
The total time of flight (T) is twice the time it takes to reach the highest point since the object takes the same amount of time to descend as it took to ascend.
T = 2 * t_highest
T = 2 * 1.53 ≈ 3.06 s
Therefore, the object will remain in the air for approximately 3.06 seconds.