An arrow is shot straight upward at 55 m/s.
a) find the time until the arrow reaches its peak
b)how high was the arrow at its peak
c)find the total time the arrow is in the air
d)what was the velocity of the arrow after 3.5 seconds
e)how high was it at 3.5 seconds
See previous post.
To find the answers to these questions, we can use the basic equations of motion under constant acceleration. In this case, the acceleration is due to gravity, which is approximately 9.8 m/s². Let's solve each question step by step:
a) To find the time until the arrow reaches its peak, we need to know the initial velocity (u) and the acceleration (a). In this case, the initial velocity is 55 m/s, and the acceleration is -9.8 m/s² (negative because it is acting in the opposite direction of the motion). We can use the equation:
v = u + at
Since the arrow reaches its peak, the final velocity (v) will be zero. So, we can rewrite the equation as:
0 = 55 + (-9.8)t
Solving for t, we get:
9.8t = 55
t = 55 / 9.8 ≈ 5.61 seconds
b) To find the height of the arrow at its peak, we can use the equation:
s = ut + (1/2)at²
Plugging in the values:
s = 55 * 5.61 + (1/2) * (-9.8) * (5.61)²
s ≈ 154.25 meters
c) The total time the arrow is in the air is twice the time to reach the peak since it takes the same amount of time to come back to the starting point. So, the total time is:
2 * 5.61 = 11.22 seconds
d) To find the velocity of the arrow after 3.5 seconds, we can use the equation:
v = u + at
Plugging in the values:
v = 55 + (-9.8) * 3.5
v ≈ 20.3 m/s
e) To find the height of the arrow at 3.5 seconds, we can use the equation:
s = ut + (1/2)at²
Plugging in the values:
s = 55 * 3.5 + (1/2) * (-9.8) * (3.5)²
s ≈ 86.98 meters
Therefore, the answers are:
a) The time until the arrow reaches its peak is approximately 5.61 seconds.
b) The height of the arrow at its peak is approximately 154.25 meters.
c) The total time the arrow is in the air is approximately 11.22 seconds.
d) The velocity of the arrow after 3.5 seconds is approximately 20.3 m/s.
e) The height of the arrow at 3.5 seconds is approximately 86.98 meters.