A lead pellet is propelled vertically upward by an air rifle so that its initial speed is 49 m/sec. Find its total time of flight.
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To find the total time of flight, we need to consider the vertical motion of the lead pellet. We can use the following steps:
1. Identify the known values:
- Initial velocity (u) = 49 m/sec (upward direction)
- Final velocity (v) = 0 m/sec (at the highest point)
- Acceleration (a) = -9.8 m/sec^2 (due to gravity, pointing downward)
- We assume that there is no air resistance.
2. Use the kinematic equation to find the time it takes to reach the highest point:
We can use the following equation, which relates the final velocity (v), initial velocity (u), acceleration (a), and time (t):
v = u + at
Since the final velocity at the highest point is 0 m/sec, the equation becomes:
0 = 49 - 9.8t
Solving this equation for time (t), we get:
9.8t = 49
t = 49 / 9.8
t = 5 sec
So, it takes 5 seconds for the pellet to reach the highest point.
3. To find the total time of flight, we need to consider the time it takes for the pellet to come back down. Since the upward and downward motions are symmetrical, the time taken to reach the highest point is equal to the time taken to come back down.
Therefore, the total time of flight is:
Total time of flight = 2 * time taken to reach the highest point
Total time of flight = 2 * 5 sec
Total time of flight = 10 sec
Thus, the total time of flight for the lead pellet is 10 seconds.