To determine how long the object will be in the air, we can analyze the vertical motion of the object. When an object is thrown straight up, it will reach its highest point and then fall back down due to the force of gravity.
The key equation for the vertical motion is:
v = u + gt
where:
- v is the final velocity (which will be -50 m/s at the highest point, considering the opposite direction to the initial velocity),
- u is the initial velocity (50 m/s),
- g is the acceleration due to gravity (-9.8 m/s²),
- t is the time.
At the highest point, the final velocity will be zero (v = 0). We can use this information to find the time it takes to reach the highest point:
0 = 50 - 9.8t
Simplifying the equation:
9.8t = 50
t = 50 / 9.8
t ≈ 5.10 seconds
Therefore, it will take approximately 5.10 seconds for the object to reach its highest point. However, the object will continue to be in the air during both the upward and downward journeys. So, to calculate the total time in the air, we need to consider the time for the complete vertical journey.
Since the object will take the same amount of time to reach the highest point and to come back down, the total time in the air can be calculated by multiplying the time to reach the highest point by 2:
Total time in the air = 2 * 5.10 seconds = 10.20 seconds
Hence, the object will be in the air for approximately 10.20 seconds.